High Resolution NMR Spectroscopy: Understanding Molecules and their Electronic Structures

By Elsevier Science

The progress in nuclear magnetic resonance (NMR) spectroscopy that took place during the last several decades is observed in both experimental capabilities and theoretical approaches to study the spectral parameters. The scope of NMR spectroscopy for studying a large series of molecular problems has notably broadened. However, at the same time, it requires specialists to fully use its potentialities. This is a notorious problem and it is reflected in the current literature where this spectroscopy is typically only used in a routine way. Also, it is seldom used in several disciplines in which it could be a powerful tool to study many problems. The main aim of this book is to try to help reverse these trends.

This book is divided in three parts dealing with 1) high-resolution NMR parameters; 2) methods for understanding high-resolution NMR parameters; and 3) some experimental aspects of high-resolution NMR parameters for studying molecular structures. Each part is divided into chapters written by different specialists who use different methodologies in their work. In turn, each chapter is divided into sections. Some features of the different sections are highlighted: it is expected that part of the readership will be interested only in the basic aspects of some chapters, while other readers will be interested in deepening their understanding of the subject dealt with in them.

• Shows how NMR parameters are useful for structure assignment as well as to obtain insight on electronic structures
• Emphasis on conceptual aspects

• Contributions by specialists who use the discussed methodologies in their everyday work

• Language: English
• Publisher: Elsevier Science
• Release date: Jun 8, 2013
• ISBN: 9780444594143

Book preview

1

Introduction

Rubén H. Contreras,    Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA, Argentina

Abstract

In this introductory chapter are described briefly the aims and scopes of this multiauthor book. One of the main ideas behind them is helping its readership to understand some approaches for extracting information on subtle chemical interactions, defining trends of such parameters from either measured or calculated high-resolution NMR parameters (indirect nuclear spin–spin coupling constants and nuclear magnetic shielding constant) without needing to acquire solid backgrounds on quantum chemistry. However, in all cases, the discussed ideas are based on solid grounds, and adequate references are quoted for readers interested in a better understanding of the basic concepts lying behind such approaches. It is highlighted that such discussions are restricted only to a few methods in order to both avoid overlapping this book with descriptions found in the current literature and to avoid lengthening this book beyond reasonable limits.

It was also considered pertinent to include chapters dealing with concepts whose importance are increasing rapidly in modern NMR spectroscopy like for instance, relativistic effects on NMR parameters in compounds containing heavy atoms, and NMR spectroscopy in paramagnetic species, pNMR.

Also, it was considered opportune including in this book excellent examples showing how very good excellent sets of experimental values can provide interesting insight in some chemical interactions.

Keywords

Scope and aims; Qualitative model; Exchange interactions; FC term; PSO term; Chemical shifts

During the past decades, there has been a very important progress in nuclear magnetic resonance spectroscopy (NMR). This progress took place both in experimental instrumentation and in theoretical approaches that help extracting invaluable molecular information from the spectral parameters commonly known as high-resolution NMR parameters (HR-NMR parameters). In this way, the scope of this spectroscopy for studying a large series of molecular problems has notably broadened. At first sight, this scenario could lead many people to wonder why a new book dealing with HR-NMR parameters is worthwhile when there are plenty of books dealing with related subjects. However, looking at that scenario from inside, it is noted that NMR spectroscopy has become a quite specialized field that requires of specialists if its potential is to be used at its best, which is the aim of this book. This is a notorious problem, and it is reflected in many scientific papers published in the current literature where this spectroscopy is only used on a routinely base. In several disciplines, where it could be used as a powerful tool to study many molecular problems, it is seldom used, narrowing notably its potential scope.

Taking into account comments made above, the main aim of this multiauthor book is intending to help reversing, at least in part, this trend, broadening notably the present scope for employing HR-NMR parameters to study a variety of molecular problems. For undertaking this task, it would be adequate to analyze first what are the main problems defining the mentioned situation. Perhaps the main reason is not difficult to be sorted out. To extract at its best possibilities electronic molecular information from HR-NMR parameters, it is required to have an interdisciplinary team of specialists to be able to (a) acquire the spectra using modern and sophisticated techniques. (b) After that comes the often not easy task of extracting and assigning HR-NMR parameters to atoms belonging to the molecular system under study. (c) From HR-NMR parameters thus found it is necessary to employ adequate approaches to extract, as much as possible, information on the electronic structure of the molecular system being studied. Without forgetting points (a) and (b), in this book are described few useful approaches to study aspects connected with point (c). The ability to extract in-depth electronic structure information from HR-NMR parameters requires of mathematical and physical backgrounds that are seldom acquired by undergraduate students in several disciplines. In fact, according to this editor’s own experience, it is observed that for graduates in several disciplines to face either a rather involved equation or to deal with a tensor property is something similar to be confronted to a monster. For this reason, in this book, emphasis is placed on points like this: even complicated equations are rather easy to be read physically after a short and adequate training is acquired, which can easily be achieved even without having a sound background either in Mathematics or in Physics. Since it is expected that this book be adequate as a textbook for either advanced undergraduate or graduate student courses in disciplines like Biology, different branches of Chemistry, Physics, or Material Sciences, all authors were asked to explain ideas requiring complex concepts in the easiest possible way keeping at the same time, a sound background.

When organizing this book the following important point was also taken into account. In many laboratories where NMR spectroscopy is not an end in itself but just a powerful tool to investigate a large series of molecular problems, it is important to obtain insight on trends of HR-NMR parameters in terms of chemical interactions affecting them. Generally, in this type of laboratories that task is usually more important than just obtaining accurately calculated values that agree well with their experimental counterparts. That is the reason why in several parts of this book HR-NMR parameter trends are described employing either qualitative or approximate approaches. In other parts of this book, some other important concepts like that of the relationship between the transmission of the FC interaction and the Fermi hole (see Ref. [7] in Chapter 8) is used to rationalize several spin–spin coupling constant (SSCC) trends. On this line of thought, it is very easy to realize that any hyperconjugative interaction becomes a kind of carrier for the spin information associated with the FC term. In turn, this conclusion helps to identify, by just observing the general configuration of a molecular system, if the FC interaction of a given SSCC is transmitted through more than one pathway between two given isotopes. This physical understanding of the Fermi hole can also lead to an easy conceptual analysis on the sign of several types of couplings mainly transmitted by exchange interactions. One conspicuous case is that of geminal couplings where, for the same types of isotopes, it is experimentally known that in some cases, it is positive and in some other cases, negative. This task is notably achieved if discussions presented in Chapter 5 are followed in detail. From that chapter, it is easy to understand that in a given molecule the overlap between two adjacent bonds (or one bond and one nonbonding electron pair) is negative at the position of their common nucleus. This indicates that interactions favoring the corresponding positive electronic cloud algebraically increase the FC term of the geminal coupling under consideration and vice versa.

Several other FC contributions that can easily be rationalized on similar grounds are briefly cited here, like the phenomenon reported many years ago, about the FC transmission by an intermediate fragment; the long-range transmission of the FC term by sequences of concatenated hyperconjugative interactions and the different signs that can be observed in JFH SSCCs mainly transmitted through space. A point that should be stressed when performing a qualitative analysis of this type is this one: in all cases when explaining concepts in easy terms, much care is taken in keeping all explanations on sound grounds.

In each chapter is included a References section, which includes some seminal works, some basic references and others that could satisfy highly motivated readers. However, an important point that should be taken into account when reading this book is this: quoted references by no means cover exhaustively the current literature corresponding to each chapter. The reason is that each chapter does not constitute a kind of a review article; in all cases, all authors intended to cover didactic aspects of each chapter contents instead of citing exhaustively the corresponding current literature. It is stressed that a huge amount of articles were not quoted not because they were considered second rate, but simply because those which were quoted referred adequately to the subject under consideration. Besides, all in all, special care was taken for the length of each chapter, not to exceed reasonable limits.

Each chapter includes an exercise section that could help understanding different concepts. Additionally, such section will be particularly useful if this book is adopted as a textbook in a course either for advanced undergraduate or for graduate students. It is important to note that the levels of those exercises are not uniform. It is expected that, when using this book as a textbook, the advice of each tutor or professor will be of particular relevance when addressing such exercises and in using them in the most appropriate way.

It is remarked that no chapter of this book deals with NMR parameters for compounds measured in anisotropic phase. This does not mean that this field is not adequately appreciated as a very valuable one whose importance is expected to continue increasing notably during the next few years. Similar advice can be made about NMR relaxation times. Also, it is important to remark that no chapter is devoted neither to describe nor to compare theoretical approaches for calculating HR-NMR parameters. Such apparent omission originates in these three important reasons: (a) the goal of avoiding significant overlap of the contents of this book with any other book dealing with HR-NMR parameters; (b) the fact that in the current literature there are excellent books and review articles dealing with this subject suggested that their adequate citations in several chapters of this book would be the best way to proceed; (c) the constraint on the length of the whole book to be kept within reasonable limits.

Chapters are written by different well-known specialists that use different methodologies and approaches in their everyday scientific works. Each chapter is divided into sections helping in this way the part of the readership that could be interested only on some basic aspects of a given subject. In such case, they could skip some sections and concentrate in those parts that the reader considers more appealing for her/his studies. On the other hand, interest can arise in going further on several other parts of the subject being read. In that case, interested readers could resort to the basic literature quoted at the end of the respective chapter. Finally, a few cross-references between chapters are marked alongside the book.

Besides comments made above, in this introductory chapter, succinct descriptions of aims and contents for different chapters are given. However, such comments do not necessarily follow the chapters’ ordering. Hence, this outlook is expected to highlight notably the coherence and the unity of the whole book, while remarking some generalized interesting conclusions. Whenever considered convenient, some relevant comments are included describing in simple terms how chemical shifts and coupling constants can be powerful indicators of some chemical interactions being present in the molecular system under consideration.

As mentioned above, all authors took care of presenting each subject taking into account didactic aspects. In this editor’s opinion, the goal has been successfully achieved. As a complementary point, most authors agreed with the editor about the usefulness of opening adequate channels for asking questions related to this book. The suggested e-mail contact is [e-mail].

First, Chapter 2 starts describing some basic aspects of electron–nucleus magnetic interactions originating the HR-NMR parameters known as nuclear magnetic shielding constants, σ(A), and indirect spin–spin coupling constants, JAB. Only aspects of these parameters corresponding to light atoms are considered in that chapter. Besides, it is assumed that the molecular system under study corresponds to a closed shell one. Furthermore, only the case where these parameters are measured in an isotropic phase is taken into account.

The expression light atoms is used here to denote atoms whose parameters are described correctly within the framework of nonrelativistic quantum chemistry. A very didactic introduction to relativistic quantum chemistry is presented in Chapter 4. This also includes its application to HR-NMR parameters. It is highly recommended for students dealing with organometallic compounds to study Chapter 4 carefully.

Although nowadays most HR-NMR spectroscopy applications correspond to closed-shell molecular systems, it is expected that in the near future this spectroscopy will also be applied to study, in an extensive way, paramagnetic compounds. For this reason, when planning the organization of this book, it was considered important to include Chapter 3, entitled Chemical Shift in Paramagnetic Systems, which is dubbed as pNMR. This is a very clearly written chapter, where an interesting set of references is given. It is noted that this subject is seldom described in the current literature, and for this reason, it was considered convenient to include a reasonable exhaustive references set in Chapter 3.

The first HR-NMR parameter mentioned above, σ(A), is closely related to chemical shift usually denoted by δ(A) for the same atomic nucleus A. This quantity is contributed by two different terms, that is, its diamagnetic, σD(A), and its paramagnetic, σP(A) parts. They are, respectively, first- and second-order terms, indicating with this terminology that, within the Raleigh–Schrödinger perturbation theory, the order that can be employed to calculate each of them. The second type of HR-NMR parameters mentioned above is observed between a pair of magnetic nuclei where the magnetic interaction between them is transmitted through the molecular electronic system. Within the nonrelativistic theory they are contributed, when measured in isotropic phase, by four terms, J(A,B) = JFC(A,B) + JPSO(A,B) + JSD(A,B) + JDSO(A,B), where only the first one, FC, is a scalar quantity (isotropic), while the only first-order quantity is JDSO(A,B), which is an anisotropic contribution, that is, a second rank tensor quantity. In some chapters, J(A,B) is referenced as J coupling constants and in other chapters is employed the common acronym SSCCs to designate them. In Chapter 7, this acronym is changed to NSSC.

Both types of parameters correspond to second rank tensors. The only exception to this last assertion is the FC term, while being a second-order quantity, it is isotropic. As already mentioned, Chapter 2 is limited to discussing HR-NMR parameters measured in an isotropic phase. A particular question seems relevant at this point, about physical properties having second rank tensor character: what is it observed when measurements of that property are carried out in an isotropic phase? Everybody having acquired basic training in Mathematics and/or Physics is expected to answer in isotropic phase only 1/3 of its trace is observed. Yes, this answer is correct; however, it is important to take into account that HR-NMR parameters are molecular parameters and most molecules are anisotropic. This fact originates a subtle effect. For instance, the trace of a given σ(A) tensor depends on the angle formed between its principal axes system, PAS, and one of the bonds containing the atom whose nuclear magnetic shielding constant is sought. This property is not frequently discussed in the current literature; in Chapter 2, the expression geometric effect is coined when referring to it. Interesting cases where this effect can easily be observed are commented in Chapter 10. Similar assertion holds for the paramagnetic spin-orbit (PSO) and spin-dipolar (SD) contributions to SSCCs.

In Chapter 2 is described a qualitative approach designed to get insight into effects caused by the different chemical interactions on any HR-NMR parameter. Its main characteristics are described in simple terms. Here it is dubbed the qualitative PP-RPA-model and comprises a full account of the most prominent interactions in Biochemistry as well as in Organic Chemistry. It is expected that anybody having a good chemical background can use it to extract chemical insight from either measured or calculated HR-NMR parameters. As mentioned above, the theory behind this qualitative model is described with important detail in Chapter 5, The Polarization Propagator Approach as a Tool to Study Electronic Molecular Structures from High-Resolution NMR Parameters. For second-order properties, each contribution within the qualitative PP-RPA model can be separated into two different systems, namely, the emission–receiver and the transmission systems. For a coupling constant, any coupled nucleus can play the emission or the receiver roles since always JAB = JBA. Moreover, for a magnetic shielding constant, the emission and the receiver systems are the same. It is noted that the electronic environment around each coupling nuclei conforms the emission–receiver system. On the other hand, for nuclear magnetic shielding constants, the emission–receiver system is determined by the electronic environment of the atom under consideration. In both cases, the transmission system corresponds to a property determined by the whole respective molecular electronic system, that is, the triplet polarization propagator matrix for FC and SD terms of SSCCs, and the singlet propagation matrix, for chemical shifts as well as for the PSO contribution to SSCCs.

One important result discussed in Chapter 10 is this: several magnetic shielding constant trends along a series of compounds are reproduced by the emission–receiver system, that is, by the electronic surroundings of the nucleus whose nuclear magnetic shielding constant is considered. In other words, according to descriptions made in Chapter 2, many chemical shifts trends are defined by perturbators (see Chapter 5).

One important question followed along this book is: How is it possible detecting transmission mechanisms for HR-NMR parameters through the molecular electronic structure? This question, at least in several cases, can also be put in the following terms: How do different chemical interactions affect a given HR-NMR parameter along a family of compounds?

In Chapter 5 are described the so-called IPPP and CLOPPA methods to detect coupling pathways for the FC term. Some applications are presented and discussed. A different approach is described in Chapter 6, where de-convoluting the FC contribution to SSCCs into natural bond orbitals, NBOs, provides insight into transmission mechanisms of the FC term. This chapter is very clearly written, and in general, important insight on SSCCs can be obtained from this approach. Students reading it will have the extra bonus of familiarizing themselves with the Weinhold et al.’s NBO approach (see Ref. [31] of Chapter 6) which is very useful for understanding, at the molecular level, many chemical properties. In Chapter 6, several other methods for understanding different multi-pathways transmissions for the FC term are also cited.

In Chapter 7 is presented a contribution entitled Electronic Current Densities Induced by Magnetic Fields and Nuclear Magnetic Dipoles. Theory and Computation of NMR Spectral Parameters. In this chapter, the known Ramsey approaches to describe electron–nucleus magnetic interactions that lead to nuclear magnetic shielding constants and to spin–spin coupling constant tensors are reformulated in terms of induced electronic current densities that follow classical electrodynamics laws. They are considered in a Quantum Mechanics context. In this way, magnetic shielding constants are expressed through quantum mechanics electronic densities. A similar description for SSCCs is presented. Such descriptions allow the author to obtain maps of nuclear magnetic shielding densities and of nuclear magnetic spin–spin coupling densities. Plots of such densities provide very interesting insights on mechanisms originating chemical shifts and SSCCs.

In Chapter 8, the qualitative PP-RPA-model, described in Chapter 2, is employed to rationalize the FC term for several SSCCs trends. It is worth mentioning the description of the so-called Perlin effect obtained using this qualitative approach. This description should be compared with that obtained in Chapter 6 using the natural J coupling method.

In Chapter 9, entitled "Non Bonded Internuclear Spin-Spin Couplings (J Couplings Through-Space) for Structural Determination in Small Organic and Organometallic Species," an interesting set of compounds where it is known experimentally that spin–spin coupling constants are transmitted between the two spatially proximate molecular fragments are discussed. Very interesting examples on this mechanism for transmitting spin–spin couplings are systematically considered.

In Chapter 10 are given examples of the qualitative PP-RPA-model versatility by applying it to rationalize how several known chemical interactions affect the nuclear magnetic shielding constants in ¹³C, ¹⁵N, ¹⁷O, and ¹⁹F isotopes. Of particular interest is to highlight the insight obtained on the steric effect corresponding to the close proximity between a methyl group and an F atom, which is experimentally known since many years ago (see references in Chapter 10) to yield a deshielding effect on the F atom. In fact, this effect is rationalized as mainly originating on paramagnetic currents involving simultaneously both proximate molecular fragments and not in perturbations of local fluorine paramagnetic currents as it could be expected. On the other hand, it is also observed that such F—H3C proximity interaction affects the diamagnetic contribution to σ(F), affecting the local diamagnetic currents but, for the same distance, its magnitude is smaller, in absolute value, than that originating in the inter-fragment paramagnetic currents. For this reason, experimentally it is observed a fluorine deshielding effect.

In many textbooks several aspects of the important chemical interaction known usually as the inductive effect are not adequately discussed to be understood for advanced students not having a good background in chemistry. Since this volume is intended to be useful as a text book for some interdisciplinary courses, it was considered pertinent to include a chapter where clear insight into that effect could nicely be appreciated. This can be found in Chapter 11 where the Authors collected a very interesting set of experimental Jcc coupling constants and use their ample chemical intuition to present this subject in an unusual clear way. Other aspects of the inductive effect are discussed in Chapter 8, where it is stressed that it does not show stereospecific behavior. This feature contrasts with hyperconjugative interactions, which show a very strong stereospecific behavior. Chapter 11 includes a brief account on how J13-C,13-C SSCCs can be measured nowadays without requiring to label compounds with ¹³C isotopes, thanks to the important progress that took place on experimental techniques when high field superconducting magnets were combined with pulsed Fourier transform techniques.

R. H. Contreras’ contributions to this book are dedicated to his grandsons Joaquín L. Tesler and Facundo M. Tesler.

Chapter 2

Brief Account of Nonrelativistic Theory of NMR Parameters

Rubén H. Contreras∗, M.B. Ferraro†, Martin C. Ruiz de Azúa‡ and Gustavo A. Aucar§,    ∗Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA, Argentina, †Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, and IFIBA, CONICET, Ciudad Universitaria, Pabellón 1 (C1428EHA), Buenos Aires, Argentina, ‡Dpto. de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Buenos Aires, Argentina, §Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina and IMIT Institute, CONICET-UNNE, Corrientes, Argentina

Abstract

This chapter describes briefly chemical shifts (or nuclear magnetic shielding constants) and indirect spin–spin coupling constants. They are well known as powerful tools for studying several molecular properties which are very important in different branches of the broad field of molecular sciences. The present description is oriented to an interdisciplinary audience and therefore it is expected that it can be followed for readers without strong backgrounds either in mathematics or physics. After a short revision of basic concepts, a qualitative method devised to extract information on electronic molecular structures is described. This aim is achieved employing this qualitative method for relating such parameters known in different series of compounds with several common chemical interactions. Since both types of NMR parameters present second-rank tensor properties, it is discussed how such property is affected in molecules measured in isotropic phase. Anybody with mathematical and physical background would answer immediately, in isotropic phase is only observed one-third of the respective tensor trace. However, in molecules that trace depends on the relative orientation of the Principal Axes System and bonds associated to the atom whose nuclear magnetic shielding is studied, or to the straight line connecting a pair of coupled nuclei. To describe these effects in this chapter is coined the expression the geometric effect to identify them. The same expression is also employed in Chapters 8 and 10. A list of exercises and appropriate references are included at the end of this chapter.

Keywords

Chemical shifts; Coupling constants; Substituent effects; PP-RPA qualitative model; Chemical interactions

1 Preliminary Considerations

In this chapter, only closed shell molecular systems containing light atoms are considered. From a didactic point of view, NMR spectroscopy provides an excellent example for a practical application of the Born–Oppenheimer approximation. In fact, in the NMR laboratory when taking the high-resolution NMR spectrum of a molecular system under study, transitions between nuclear spin states described by the Hamiltonian for nuclear states shown in Eq. (1) are induced

(1)

. The terms in the second sum correspond to expressions that are bilinear in pairs of nuclear spins. These features are important when applying perturbation theory to calculate high-resolution NMR parameters.

In Eq. (1), γA is the magnetogyric ratio of nucleus A is the nuclear magnetic shielding constant second-rank tensor of nucleus Ais the corresponding direct SSCC second-rank tensor. For the sake of simplifying typography, these are designated as σ(A), JAB, and DAB, respectively. Since the latter is purely anisotropic, when taking an NMR spectrum in isotropic phase, line positions are not affected by this interaction. Moreover, since it only depends on internuclear distances and their relative orientations, it does not provide information on the molecular electronic structure, although it can provide information on internuclear distances. However, the so-called residual dipolar couplings are very important for studying structures, particularly in macromolecules [1].

To study molecular electronic structures by measuring high-resolution NMR parameters requires understanding how electron–nucleus magnetic interactions originate the σ(A) and JAB second-rank tensors. To this end, it is resorted again to the Born–Oppenheimer approximation considering the electronic part of the molecular system under study as described by the Hamiltonian shown in Eq. (2).

(2)

and the magnetic field originating in the nuclear magnetic moments. It is stressed that in this chapter are not considered relativistic effects on NMR parameters. These effects are discussed in Chapter 4.

A discussion on σ(A) and JAB tensors is presented in Sections 2 and 3, respectively. Based on physical considerations, it is easy to understand that these tensors can be calculated via Rayleigh–Schrödinger perturbation theory [2]. In fact, in Eq. (1), it is noted that energy differences between hydrogen nuclear Zeeman levels and the ground state correspond to photons in the range of 6 × 10⁸ Hz for a magnetic field B0 ≈ 14 T, while photons due to transitions between molecular electronic levels are in the UV–visible region of the electromagnetic spectrum, that is, their photons are at least in the 10¹⁴ Hz range. This simple test shows that such parameters can be calculated resorting to perturbation theory.

Here, a qualitative approach for analyzing high-resolution NMR parameters is briefly described and subsequently applied both in this chapter and also in Chapters 8 and 10 of this book. It is a valuable tool to complement theoretical and/or experimental determinations and provides insight into fine details of molecular electronic structures, broadening notably the scope of this spectroscopy. It is hoped that this new insight will be useful for both advanced undergraduate and graduate students in a variety of disciplines including biology, chemistry, biochemistry, materials science, and physics. It is hoped that it will also help many NMR spectroscopy practitioners in obtaining a deeper insight into the problems they are studying.

For analyzing SSCCs, nJAB, it is considered that one of the coupling nuclei involved in it behaves like the emitting nucleus and the other as the receiving nucleus and they are connected by a transmission mechanism. Since always nJAB = nJBA, any of both nuclei plays one of the former two roles [3]. Analytical expressions satisfying this condition are well known when SSCCs are expressed in terms of the polarization propagator (PP) formalism considered at the random phase approximation (RPA) [4] (see Chapter 5). Therefore, such expressions seem to be an adequate starting point for performing a qualitative analysis of the principal interactions defining a given trend (either theoretical or experimental) in a series of compounds. It is strongly emphasized that no calculations at the RPA level are performed in these analyses. The PP-RPA expressions provide only a guide for spotting the main interactions defining a given trend, and in many cases, it can be discriminated if such trend originates either in the emitter and receiver or in the transmission mechanisms systems. They are particularly important in the former system, which strongly depends on even small changes in the electronic surroundings of both coupled nuclei. Doubtlessly, it is expected that, in most cases, this analysis is accompanied by the actual calculation of nJAB performed using an appropriate level of theory. In this chapter, emphasis is placed on the qualitative aspects of these parameters since there are many excellent works dealing with different levels of calculations [5].

For analyzing σ(A) shielding tensors, a similar formal approach is applied, and in this case, it is possible to consider as if both the emitting and the receiving nuclei are the same. Also in this case, no actual calculations are performed at the RPA level. Here again, the PP-RPA expressions for σ(A) are only used as a guide to spot the main factors affecting either the emitting-receiving factor or the PP matrix.

2 Comments on the Magnetic Shielding Tensor,

tensor are obtained by recalling that the first term in Eq. (1) is bilinear both in magnetic nuclear moments and the spectrometer magnetic field (Eq. 3)

(3)

which leads to the following perturbation operators

(4a)

(4b)

(4c)

is the kth electron vector position from the origin of the vector potential (gauge origin, here taken as the coordinates origin, (Ois the position of the same electron measured from nucleus A, whose magnetic shielding tensor is under consideration. Lkα and LkAα are the Cartesian α components of the angular momentum of electron k with respect to an arbitrary origin of coordinates and with respect to nucleus A, respectively. Operators (, while operator (4b) does not depend on that origin.

.

The magnetic interaction has this striking feature: the gauge origin can be arbitrarily chosen to be in any point, for example, the origin of coordinates, or the center of mass (CM), or the nucleus of interest. It can be shown that, even though paramagnetic and diamagnetic contributions to σ(A) are different depending on the origin choice, their total sum, σD(A) + σP(A), which is the physical observable (i.e., what it is measured), does not depend on that choice. This freedom to choose the gauge origin can be used in a theoretical analysis to either facilitate σ calculations or to get particular insight into their transmission mechanisms.

Hamiltonian H(1,0) in Eq. (4b) describes the paramagnetic interaction with the nucleus of interest. It can also be thought of as inducing an orbital current, but in this case the gauge origin is clearly defined by the atom whose σ = σD + σP shielding tensor is under study. Intuitively, this means that the easier the electrons can be put into rotation, the larger the magnetic effect. These qualitative features are helpful for obtaining insight into both the paramagnetic and diamagnetic terms.

There is a particular connection between the paramagnetic contribution σP and a totally independent magnetic effect. The nuclear spin couples to the molecular rotation in absence of an external B0 and emits electromagnetic radiation in the microwave spectral region [6]. That molecular rotation drifts the electron cloud yielding on average an electronic orbital current around the molecular CM. If σP . Therefore, under these conditions, a strict equivalence of the paramagnetic effect holds for both parameters. The equivalence of these two totally independent spectral parameters has been exploited to obtain experimentally accurate values of σP. The diamagnetic contribution, σD, can also be calculated at the CM, by the more accurate first-order than second-order perturbation theory, getting a very precise determination of the absolute shielding for small molecules. It is highlighted that the above-mentioned equivalence does no longer hold for relativistic electrons, since in this case the paramagnetic interaction and molecular rotation effects are not described by the same physical operator.

The gauge invariance character of operator (4b) is not frequently highlighted in the current literature. It is shown below that this fact is very useful for studying some aspects of electronic molecular structures. In fact, a careful physical reading of operator (4b) can help significantly in rationalizing σ trends in series of compounds. In isotopes like, for example, ¹⁵N, ¹⁷O, and ¹⁹F, this term is very sensitive to spatially proximate interactions, that is, to small changes in its local electronic environment. As commented below, SSCCs can also be quite sensitive to proximate interactions. This important application of NMR parameters as probes to detect even small changes in a local electronic distribution makes this spectroscopy very useful to study a wide variety of problems in different branches of the molecular sciences. The main aim of this chapter is to show to nonspecialists in quantum chemistry that they can benefit from this spectroscopy in a much wider way than just using either a few empirical correlations or a few calculations with computational programs currently available in the literature. However, care is taken in making this description based on a sound theoretical background. Although there are many examples where changes in NMR parameters are used to detect proximate interactions, here this example is quoted. At present, ribonucleic acids are labeled with fluorine atoms [7], and the corresponding ¹⁹F NMR parameters provide information on its electronic surroundings, providing information on subjects like, for example, some features of binding sites or the folding nature of some macromolecules. It is highlighted that the natural abundance of ¹⁹F is 100%, its nuclear spin is ½, and its nuclear quadrupole moment is zero, as it happens with all ½ spin isotopes. There is an additional advantage for using ¹⁹F as a marker for large biological compounds, that is, its ample range of chemical shifts. This last feature is shared with ¹⁷O, but its nuclear quadrupole moment is about—5 × 10− 3 in 10− 28 m² units, and its natural abundance is very low, 3.7 × 10− 2%. To some extent such chemical shift feature is also shared by ¹⁵N (spin ½ and natural abundance 3.65 × 10− 1%). Some reasons for these large spreads in their chemical shift ranges are discussed below. A few examples of chemical shifts sensitivity to small electronic molecular structure changes are discussed in Chapter