Computational Chemistry in Nuclear Magnetic Resonance

Determining molecular structure via nuclear magnetic resonance (NMR) spectral analysis has become an integral part of physical–chemical research in organic and inorganic chemistry. While NMR analysis can be complemented by other physical chemistry experimental techniques of structure elucidation, such as mass spectrometry (MS), infrared (IR) or Raman spectroscopy, X-ray crystallography, etc., applying computational chemistry to NMR spectra modeling remains vital. Utilizing high-quality calculations of NMR chemical shifts and indirect nuclear spin–spin coupling constants for various chemical structures helps eliminate ambiguity, especially when investigating newly synthesized compounds giving NMR signals beyond the typical ranges.

Since Ramsey applied perturbation theory to NMR properties in the 1950s, computational methodology has made great strides due to both the accelerated progress of computer technology and the development of the electron theory. The density functional theory (DFT) methods attract significant attention today being successfully applied to studying macromolecules of biological interest. Moreover, ab initio wavefunction-based correlated methods, systematically accounting for electron correlation effects, such as polarization propagator (PP) approaches and coupled-cluster (CC) methods, are now routinely applied for calculating the NMR properties of small- and medium-sized molecules. Overall, computational chemistry in application to NMR analysis has become an imminent tool for unequivocal determination of chemical structures.

This Special Issue of Magnetochemistry, entitled “Computational Chemistry in Nuclear Magnetic Resonance”, is dedicated to showcasing recent advances in the field of NMR quantum chemistry methods and vivid examples of their application to NMR spectra modeling. It comprises six papers authored by eminent researchers active in this field (three research articles and three review articles).

The first paper, “Extending NMR Quantum Computation Systems by Employing Compounds with Several Heavy Metals as Qubits” [1], is authored by Jéssica Boreli dos Reis Lino (from Federal University of Lavras, Brazil), Mateus Aquino Gonçalves (from Federal University of Lavras, Brazil), Stephan P. A. Sauer (from University of Copenhagen, Denmark), and Teodorico Castro Ramalho (from Federal University of Lavras, Brazil and University Hradec Kralove, Czech Republic). It considers the NMR technique as an experimental quantum simulator, where nuclear spins are employed as quantum bits or qubits. The paper reports on the study of four heavy metal complexes representing possible candidates for NMR-based quantum information processing (NMR-QIP) implementations. These complexes include NMR-active nuclei such as ¹¹³Cd, ¹⁹⁹Hg, ¹²⁵Te, and ⁷⁷Se assembled with the most commonly employed nuclei in NMR-QIP implementations (¹H, ¹³C, ¹⁹F, ²⁹Si, and ³¹P). The authors have tested these four complexes to ensure they have the spectral properties required for efficient NMR-QIP implementations. Specifically, the results showed that the calculated NMR spin–spin coupling constants were so large in magnitude as to allow efficient two-qubit operations which preserve coherence and increase the speed of quantum gate operations. The range of NMR chemical shifts for such systems was found to be wide enough to implement selective manipulation of the individual spins, i.e., to accomplish the qubit addressability. The nuclear relaxation times were estimated as sufficiently large in magnitude to implement the logic quantum gates in certain NMR-QIP algorithms. All calculations were performed using the state-of-the-art relativistic two-component spin–orbit zeroth-order regular approximation (ZORA) method as implemented in DFT.

The second contribution, “Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances” [2] by Irina L. Rusakova (from A. E. Favorsky Irkutsk Institute of Chemistry, Russia), is a review paper summarizing the fundamentals of the nonrelativistic and relativistic theories of nuclear magnetic resonance parameters and discussing the most popular modern computational methodologies used today for quantum chemical modeling of NMR spectra, with special attention paid to recent advances in this field. Among the considered quantum chemical methods for calculating NMR parameters are configuration interaction (CI) methods, various CC models, DFT methods (including generalized relativistic four-component representation of the NMR parameters within the Dirac–Kohn–Sham formalism), PP methods, and many-body perturbation theory (MBPT) methods. Separate discussions of specialized basis sets for calculating spin–spin coupling constants and chemical shifts, vibrational corrections, and solvation models are included in the last few sections of the review. The review is extremely thorough and encompasses as many as 684 references.

The third paper, “The Structure of Biologically Active Functionalized Azoles: NMR Spectroscopy and Quantum Chemistry” [3] by Lyudmila I. Larina (from A. E. Favorsky Irkutsk Institute of Chemistry, Russia), is a review paper that gathers the data on the stereochemical structure of functionalized azoles (pyrazoles, imidazoles, triazoles, thiazoles, and benzazoles) and related compounds obtained via multipulse and multinuclear (¹H, ¹³C, and ¹⁵N) NMR spectroscopy and quantum chemistry. The review contains vivid examples of the combined NMR experimental and computational quantum chemical study of stereochemical behavior of nitrogen-containing heteroaromatic and heterocyclic compounds.

The fourth contribution, “Relativistic Effects from Heavy Main Group p-Elements on the NMR Chemical Shifts of Light Atoms: From Pioneering Studies to Recent Advances” [4] by Irina L. Rusakova and Yuriy Yu. Rusakov (from A. E. Favorsky Irkutsk Institute of Chemistry, Russia), is a review paper that represents a compendium of computational studies of relativistic effects on the NMR chemical shifts of light nuclei caused by the presence of heavy main group p-block elements in molecules, i.e., the HALA effect. The majority of the review comprises a survey on the relativistic calculations of the NMR shielding constants of popular NMR-active light nuclei, such as ¹H, ¹³C, ¹⁹F, ²⁹Si, ¹⁵N, and ³¹P, in compounds containing heavy p-elements. A special focus is placed on the relativistic effects initiated by the 16th and 17th group elements. Different factors governing the behavior of the relativistic effects on the chemical shifts of light atoms are discussed. In particular, the stereochemistry of the relativistic HALA effect and the influence of the spin–orbit relativistic effects on the vibrational corrections to the shielding constants of light nuclei are considered.

The fifth paper, “The Importance of Solvent Effects in Calculations of NMR Coupling Constants at the Doubles Corrected Higher Random-Phase Approximation” [5] by Louise Møller Jessen (from University of Copenhagen, Denmark), Peter Reinholdt (from University of Southern Denmark, Denmark), Jacob Kongsted (from University of Southern Denmark, Denmark) and Stephan P. A. Sauer (from University of Copenhagen, Denmark), proposes an implementation of the polarizable continuum solvation model (PCM) for the doubles-corrected higher random-phase approximation (HRPA(D)) and the second-order polarization propagator approach (SOPPA) methods (the PCM-HRPA(D)/RPA and PCM-SOPPA/RPA) to calculate nuclear spin-spin coupling constants within the Dalton program [6]. These models assume that static solvent response effects are treated at the HRPA(D) or SOPPA level, respectively, while dynamic solvent response effects are evaluated at the random-phase approximation (RPA) level. The authors have tested their models on as many as 242 NMR spin–spin coupling constants in 20 molecules and found that their implementation works well. However, it was shown that the DFT (PBE0) level surpasses in accuracy the HRPA(D) model for most types of spin–spin coupling constants, except for ³J_HH, where HRPA(D) demonstrated the best results. The authors also have found that the direct and indirect solvent effects on spin–spin coupling constants are additive for all the methods studied, and they are almost independent of the employed computational method.

The final sixth paper in this Special Issue, “¹³C NMR Chemical Shifts of Saccharides in the Solid State: A Density Functional Theory Study” [7] by Hadeel Moustafa, Flemming H. Larsen, Anders Ø. Madsen, and Stephan P. A. Sauer (all authors from the University of Copenhagen, Denmark), reports on the theoretical investigation of the ¹³C NMR chemical shifts for several mono-, di- and tri-saccharides in the solid state. The paper mainly focuses on the study of differences in the ¹³C chemical shifts in mono- and poli-saccharides calculated with and without water molecules in the unit cell, and on the changes in the chemical shifts upon the formation of di- and tri-saccharides. This is the only work in this Special Issue that reports on the solid-state NMR calculations, performed within the DFT method in combination with the gauge including -projector augmented wave (GIPAW) method. The authors have found that the largest changes in the carbon chemical shifts (including the changes in the isotropic chemical shifts) for the atoms involved in the glycosidic linkage are reaching up to 14 ppm upon the transition from monosaccharides to disaccharides. At the same time, the changes occurring in the carbon chemical shifts when transitioning from disaccharides to the tri-saccharides were somewhat smaller. For crystals containing water molecules, the authors observed that ¹³C NMR isotropic chemical shifts for atoms in close vicinity to the crystal water molecules differ from those for the corresponding anhydrate analogies by about 2–5 ppm. The established changes in carbon chemical shifts showed no evident correlation with the distance of atoms under consideration from the crystal water molecules.

This Special Issue represents a valuable contribution to the field of computational NMR. We would like to sincerely thank all of the authors who contributed to this Special Issue for their dedicated efforts and the prominent quality of their papers. We would also like to express our gratitude for the timely support of the editorial team of Magnetochemistry, whose assistance has helped the guest editor to compose and prepare this Special Issue.