Structural and dynamic effects of pseudouridine modifications on noncanonical interactions in RNA.

Pseudouridine is the most frequently naturally occurring RNA modification, found in all classes of biologically functional RNAs. Compared to uridine, pseudouridine contains an additional hydrogen bond donor group and is therefore widely regarded as a structure stabilizing modification. However, the effects of pseudouridine modifications on the structure and dynamics of RNAs have so far only been investigated in a limited number of different structural contexts. Here, we introduced pseudouridine modifications into the U-turn motif and the adjacent U:U closing base pair of the neomycin-sensing riboswitch (NSR)-an extensively characterized model system for RNA structure, ligand binding, and dynamics. We show that the effects of replacing specific uridines with pseudouridines on RNA dynamics crucially depend on the exact location of the replacement site and can range from destabilizing to locally or even globally stabilizing. By using a combination of NMR spectroscopy, MD simulations and QM calculations, we rationalize the observed effects on a structural and dynamical level. Our results will help to better understand and predict the consequences of pseudouridine modifications on the structure and function of biologically important RNAs.

Multiscale Modeling of Phosphate···π Contacts in RNA U-Turns Exposes Differences between Quantum-Chemical and AMBER Force Field Descriptions.

Phosphate···π, also called anion···π, contacts occur between nucleobases and anionic phosphate oxygens (OP2) in r(GNRA) and r(UNNN) U-turn motifs (N = A,G,C,U; R = A,G). These contacts were investigated using state-of-the-art quantum-chemical methods (QM) to characterize their physicochemical properties and to serve as a reference to evaluate AMBER force field (AFF) performance. We found that phosphate···π interaction energies calculated with the AFF for dimethyl phosphate···nucleobase model systems are less stabilizing in comparison with double-hybrid DFT and that minimum contact distances are larger for all nucleobases. These distance stretches are also observed in large-scale AFF vs QM/MM computations and classical molecular dynamics (MD) simulations on several r(gcGNRAgc) tetraloop hairpins when compared to experimental data extracted from X-ray/cryo-EM structures (res. ≤ 2.5 Å) using the WebFR3D bioinformatic tool. MD simulations further revealed shifted OP2/nucleobase positions. We propose that discrepancies between the QM and AFF result from a combination of missing polarization in the AFF combined with too large AFF Lennard-Jones (LJ) radii of nucleobase carbon atoms in addition to an exaggerated short-range repulsion of the r-12 LJ repulsive term. We compared these results with earlier data gathered on lone pair···π contacts in CpG Z-steps occurring in r(UNCG) tetraloops. In both instances, charge transfer calculations do not support any significant n → π* donation effects. We also investigated thiophosphate···π contacts that showed reduced stabilizing interaction energies when compared to phosphate···π contacts. Thus, we challenge suggestions that the experimentally observed enhanced thermodynamic stability of phosphorothioated r(GNRA) tetraloops can be explained by larger London dispersion.

Short-Range Imbalances in the AMBER Lennard-Jones Potential for (Deoxy)Ribose···Nucleobase Lone-Pair···π Contacts in Nucleic Acids.

The lone-pair···π (lp···π) (deoxy)ribose···nucleobase stacking is a recurring interaction in Z-DNA and RNAs that is characterized by sub-van der Waals lp···π contacts (<3.0 Å). It is a part of the structural signature of CpG Z-step motifs in Z-DNA and r(UNCG) tetraloops that are known to behave poorly in molecular dynamics (MD) simulations. Although the exact origin of the MD simulation issues remains unclear, a significant part of the problem might be due to an imbalanced description of nonbonded interactions, including the characteristic lp···π stacking. To gain insights into the links between lp···π stacking and MD, we present an in-depth comparison between accurate large-basis-set double-hybrid Kohn-Sham density functional theory calculations DSD-BLYP-D3/ma-def2-QZVPP (DHDF-D3) and data obtained with the nonbonded potential of the AMBER force field (AFF) for NpN Z-steps (N = G, A, C, and U). Among other differences, we found that the AFF overestimates the DHDF-D3 lp···π distances by ∼0.1-0.2 Å, while the deviation between the DHDF-D3 and AFF descriptions sharply increases in the short-range region of the interaction. Based on atom-in-molecule polarizabilities and symmetry-adapted perturbation theory analysis, we inferred that the DHDF-D3 versus AFF differences partly originate in identical nucleobase carbon atom Lennard-Jones (LJ) parameters despite the presence/absence of connected electron-withdrawing groups that lead to different effective volumes or vdW radii. Thus, to precisely model the very short CpG lp···π contact distances, we recommend revision of the nucleobase atom LJ parameters. Additionally, we suggest that the large discrepancy between DHDF-D3 and AFF short-range repulsive part of the interaction energy potential may significantly contribute to the poor performances of MD simulations of nucleic acid systems containing Z-steps. Understanding where, and if possible why, the point-charge-type effective potentials reach their limits is vital for developing next-generation FFs and for addressing specific issues in contemporary MD simulations.

Quantum Chemistry Common Driver and Databases (QCDB) and Quantum Chemistry Engine (QCEngine): Automation and interoperability among computational chemistry programs.

Community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.

Surprisingly broad applicability of the cc-pVnZ-F12 basis set for ground and excited states.

Excellent convergence properties for the (aug-)cc-pVnZ-F12 basis set family, purpose-made for explicitly correlated calculations, are demonstrated with conventional wave function methods and Kohn-Sham density functional theory for various ground and excited-state calculations. Among the ground-state properties studied are dipole moments, covalent bond lengths, and interaction and reaction energies. For excited states, we looked at vertical excitation energies, UV absorption, and excited-state absorption spectra. Convergence is compared against the basis sets cc-pVnZ, def2-nVD, aug-pcseg-n, and nZaPa-NR. It is established that the cc-pVnZ-F12 family consistently yields results of n + 1 quality and better. Especially, the cc-pVDZ-F12 basis set is found to be a basis set of good cost vs performance trade-off.

Psi4 1.4: Open-source software for high-throughput quantum chemistry.

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

An intricate balance of hydrogen bonding, ion atmosphere and dynamics facilitates a seamless uracil to cytosine substitution in the U-turn of the neomycin-sensing riboswitch.

The neomycin sensing riboswitch is the smallest biologically functional RNA riboswitch, forming a hairpin capped with a U-turn loop-a well-known RNA motif containing a conserved uracil. It was shown previously that a U→C substitution of the eponymous conserved uracil does not alter the riboswitch structure due to C protonation at N3. Furthermore, cytosine is evolutionary permitted to replace uracil in other U-turns. Here, we use molecular dynamics simulations to study the molecular basis of this substitution in the neomycin sensing riboswitch and show that a structure-stabilizing monovalent cation-binding site in the wild-type RNA is the main reason for its negligible structural effect. We then use NMR spectroscopy to confirm the existence of this cation-binding site and to demonstrate its effects on RNA stability. Lastly, using quantum chemical calculations, we show that the cation-binding site is altering the electronic environment of the wild-type U-turn so that it is more similar to the cytosine mutant. The study reveals an amazingly complex and delicate interplay between various energy contributions shaping up the 3D structure and evolution of nucleic acids.

Short but Weak: The Z-DNA Lone-Pair⋠⋠⋠π Conundrum Challenges Standard Carbon Van der Waals Radii.

Current interest in lone-pair⋅⋅⋅π (lp⋅⋅⋅π) interactions is gaining momentum in biochemistry and (supramolecular) chemistry. However, the physicochemical origin of the exceptionally short (ca. 2.8 Å) oxygen-to-nucleobase plane distances observed in prototypical Z-DNA CpG steps remains unclear. High-level quantum mechanical calculations, including SAPT2+3 interaction energy decompositions, demonstrate that lp⋅⋅⋅π contacts do not result from n→π* orbital overlaps but from weak dispersion and electrostatic interactions combined with stereochemical effects imposed by the locally strained structural context. They also suggest that the carbon van der Waals (vdW) radii, originally derived for sp3 carbons, should not be used for smaller sp2 carbons attached to electron-withdrawing groups. Using a more adapted carbon vdW radius results in these lp⋅⋅⋅π contacts being no longer of the sub-vdW type. These findings challenge the whole lp⋅⋅⋅π concept that refers to elusive orbital interactions that fail to explain short interatomic contact distances.

Exploring Nature and Predicting Strength of Hydrogen Bonds: A Correlation Analysis Between Atoms-in-Molecules Descriptors, Binding Energies, and Energy Components of Symmetry-Adapted Perturbation Theory.

This work studies the underlying nature of H-bonds (HBs) of different types and strengths and tries to predict binding energies (BEs) based on the properties derived from wave function analysis. A total of 42 HB complexes constructed from 28 neutral and 14 charged monomers were considered. This set was designed to sample a wide range of HB strengths to obtain a complete view about HBs. BEs were derived with the accurate coupled cluster singles and doubles with perturbative triples correction (CCSD(T))(T) method and the physical components of the BE were investigated by symmetry-adapted perturbation theory (SAPT). Quantum theory of atoms-in-molecules (QTAIM) descriptors and other HB indices were calculated based on high-quality density functional theory wave functions. We propose a new and rigorous classification of H-bonds (HBs) based on the SAPT decomposition. Neutral complexes are either classified as "very weak" HBs with a BE ≥ -2.5 kcal/mol that are mainly dominated by both dispersion and electrostatic interactions or as "weak-to-medium" HBs with a BE varying between -2.5 and -14.0 kcal/mol that are only dominated by electrostatic interactions. On the other hand, charged complexes are divided into "medium" HBs with a BE in the range of -11.0 to -15.0 kcal/mol, which are mainly dominated by electrostatic interactions, or into "strong" HBs whose BE is more negative than -15.0 kcal/mol, which are mainly dominated by electrostatic together with induction interactions. Among various explored correlations between BEs and wave function-based HB descriptors, a fairly satisfactory correlation was found for the electron density at the bond critical point (BCP; ρBCP ) of HBs. The fitted equation for neutral complexes is BE/kcal/mol = - 223.08 × ρBCP /a. u. + 0.7423 with a mean absolute percentage error (MAPE) of 14.7%, while that for charged complexes is BE/kcal/mol = - 332.34 × ρBCP /a. u. - 1.0661 with a MAPE of 10.0%. In practice, these equations may be used for a quick estimation of HB BEs, for example, for intramolecular HBs or large HB networks in biomolecules. © 2019 Wiley Periodicals, Inc.

Interactions between cyclic nucleotides and common cations: an ab initio molecular dynamics study.

We present the first, to the best of our knowledge, ab initio molecular dynamics (AIMD) investigation on three aqueous solutions where an abasic cyclic nucleotide model is solvated in the presence of distinct cations (i.e., Na+, K+ and Mg2+). We elucidate the typical modalities of interaction between those ionic species and the nucleotide moiety by first-principles numerical simulations, starting from an inner-shell binding configuration on a time scale of 100 ps (total simulation time of ∼600 ps). Whereas the strong "structure-maker" Mg2+ is permanently bound to one of the two oxygen atoms of the phosphate group of the nucleotide model, Na+ and K+ show binding times τb of 65 ps and 10-15 ps, respectively, thus reflecting their chemical nature in aqueous solutions. Furthermore, we qualitatively relate these findings to approximate free-energy barriers of the cations' unbinding obtained by means of exploratory well-tempered metadynamics. With the aim of shedding light on the features of commonly employed force-fields (FFs), classical MD simulations (almost 200 trajectories with a total simulation time of ∼18 µs) using the biomolecular AMBER FF are also reported. By choosing several combinations of the parametrization for the water environment (i.e., TIP3P, SPC/E and OPC) and cations (i.e., Joung-Cheatham, Li-Merz 12-6 and Li-Merz 12-6-4), we found significant differences in the radial distribution functions and residence times compared to the ab initio results. The Na+ and K+ ions wrongly show quasi-identical radial distribution functions and the Li & Merz 12-6-4 Lennard-Jones parameters for Mg2+ were found to be essential in quickly reaching the binding state consistent with AIMD.

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking.

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.

Nonenzymatic Oligomerization of 3',5'-Cyclic CMP Induced by Proton and UV Irradiation Hints at a Nonfastidious Origin of RNA.

We report that 3',5'-cyclic CMP undergoes nonenzymatic di- and trimerization at 20 °C under dry conditions upon proton or UV irradiation. The reaction involves stacking of the cyclic monomers and subsequent polymerization through serial transphosphorylations between the stacked monomers. Proton- and UV-induced oligomerization of 3',5'-cyclic CMP demonstrates that pyrimidines-similar to purines-might also have taken part in the spontaneous generation of RNA under plausible prebiotic conditions as well as in an extraterrestrial context. The observed polymerization of naturally occurring 3',5'-cyclic nucleotides supports the possibility that the extant genetic nucleic acids might have originated by way of a straight Occamian path, starting from simple reactions between plausibly preactivated monomers.

Water-chromophore electron transfer determines the photochemistry of cytosine and cytidine.

Many of the UV-induced phenomena observed experimentally for aqueous cytidine were lacking the mechanistic interpretation for decades. These processes include the substantial population of the puzzling long-lived dark state, photohydration, cytidine to uridine conversion and oxazolidinone formation. Here, we present quantum-chemical simulations of excited-state spectra and potential energy surfaces of N1-methylcytosine clustered with two water molecules using the second-order approximate coupled cluster (CC2), complete active space with second-order perturbation theory (CASPT2), and multireference configuration interaction with single and double excitation (MR-CISD) methods. We argue that the assignment of the long-lived dark state to a singlet nπ* excitation involving water-chromophore electron transfer might serve as an explanation for the numerous experimental observations. While our simulated spectra for the state are in excellent agreement with experimentally acquired data, the electron-driven proton transfer process occurring on the surface may initiate the subsequent damage in the vibrationally hot ground state of the chromophore.

Towards biochemically relevant QM computations on nucleic acids: controlled electronic structure geometry optimization of nucleic acid structural motifs using penalty restraint functions.

Recent developments in dispersion-corrected density functional theory methods allow for the first time the description of large fragments of nucleic acids (hundreds of atoms) with an accuracy clearly surpassing the accuracy of common biomolecular force fields. Such calculations can significantly improve the description of the potential energy surface of nucleic acid molecules, which may be useful for studies of molecular interactions and conformational preferences of nucleic acids, as well as verification and parameterization of other methods. The first of such studies, however, demonstrated that successful applications of accurate QM calculations to larger nucleic acid building blocks are hampered by difficulties in obtaining geometries that are biochemically relevant and are not biased by non-native structural features. We present an approach that can greatly facilitate large-scale QM studies on nucleic acids, namely electronic structure geometry optimization of nucleic acid fragments utilizing a penalty function to restrain key internal coordinates with a specific focus on the torsional backbone angles. This work explores the viability of these restraint optimizations for DFT-D3, PM6-D3H and HF-3c optimizations on a set of examples (a UpA dinucleotide, a DNA G-quadruplex and a B-DNA fragment). Evaluation of different penalty function strengths reveals only a minor system-dependency and reasonable restraint values range from 0.01 to 0.05 Eh rad(-2) for the backbone torsions. Restraints are crucial to perform the QM calculations on biochemically relevant conformations in implicit solvation and gas phase geometry optimizations. The reasons for using restrained instead of constrained or unconstrained optimizations are explained and an open-source external optimizer is provided.

Investigating inclusion complexes using quantum chemical methods.

Quantum chemistry has firmly established itself as a reliable method for investigating present-day problems in biological and materials chemistry. Understanding inclusion complexes represents one of the cutting edges of simulation sciences. In this tutorial review, we focus on the role and composition of non-covalent interactions, which are essential when studying inclusion complexes. A selected set of recently developed pragmatic methods used to study inclusion complexes are then surveyed including e.g. dispersion corrected DFT, double-hybrid functionals and spin-component scaled MP2. Finally, three case studies are outlined: (a) endohedral fullerene complexes, (b) buckyball catcher and (c) resorcinarene capsule. These case studies were carefully chosen to help illustrate how one may accurately investigate inclusion complexes, at a modest computational cost, using state-of-the-art quantum chemical methods (67 references).

Why the standard B3LYP/6-31G* model chemistry should not be used in DFT calculations of molecular thermochemistry: understanding and correcting the problem.

We analyze the error compensations that are responsible for the relatively good performance of the popular B3LYP/6-31G* model chemistry for molecular thermochemistry. We present the B3LYP-gCP-D3/6-31G* scheme, which corrects for missing London dispersion and basis set superposition error (BSSE) in a physically sound manner. Benchmark results for the general main group thermochemistry, kinetics, and noncovalent interactions set (GMTKN30) are presented. A detailed look is cast on organic reactions of several arenes with C(60), Diels-Alder reactions, and barriers to [4 + 3] cycloadditions. We demonstrate the practical advantages of the new B3LYP-gCP-D3/6-31G* scheme and show its higher robustness over standard B3LYP/6-31G*. B3LYP-gCP-D3/6-31G* is meant to fully substitute standard B3LYP/6-31G* calculations in the same black-box sense at essentially no increase in computational cost. The energy corrections are made available by a Web service ( http://www.thch.uni-bonn.de/tc/gcpd3 ) and by freely available software.

A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems.

A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model chemistry yields MAD=0.68 kcal/mol, which represents a huge improvement over plain B3LYP/6-31G* (MAD=2.3 kcal/mol). Application of gCP-corrected B97-D3 and HF-D3 on a set of large protein-ligand complexes prove the robustness of the method. Analytical gCP gradients make optimizations of large systems feasible with small basis sets, as demonstrated for the inter-ring distances of 9-helicene and most of the complexes in Hobza's S22 test set. The method is implemented in a freely available FORTRAN program obtainable from the author's website.

Benchmarking density functional methods against the S66 and S66x8 datasets for non-covalent interactions.

Dispersion-corrected density functional theory is assessed on the new S66 and S66x8 benchmark sets for non-covalent interactions. In total, 17 different density functionals are evaluated. Two flavors of our latest additive London-dispersion correction DFT-D3 and DFT-D3(BJ), which differ in their short-range damping functions, are tested. In general, dispersion corrections are again shown to be crucial to obtain reliable non-covalent interaction energies and equilibrium distances. The corrections strongly diminish the performance differences between the functionals, and in summary most dispersion-corrected methods can be recommended. DFT-D3 and DFT-D3(BJ) also yield similar results but for most functionals and intermolecular distances, the rational Becke-Johnson scheme performs slightly better. Particularly, the statistical analysis for S66x8, which covers also non-equilibrium complex geometries, shows that the Minnesota class of functionals is also improved by the D3 scheme. The best methods on the (meta-)GGA or hybrid- (meta-)GGA level are B97-D3, BLYP-D3(BJ), PW6B95-D3, MPW1B95-D3 and LC-ωPBE-D3. Double-hybrid functionals are the most accurate and robust methods, and in particular PWPB95-D3 and B2-PLYP-D3(BJ) can be recommended. The best DFT-D3 and DFT-D3(BJ) approaches are competitive to specially adapted perturbation methods and clearly outperform standard MP2. Comparisons between S66, S22 and parts of the GMTKN30 database show that the S66 set provides statistically well-behaved data and can serve as a valuable tool for, for example, fitting purposes or cross-validation of other benchmark databases.

Ring-expanded bicyclic ß-lactams: a structure-chiroptical properties relationship investigation by experiment and calculations.

In the present work, the validity of the helicity rule relating the absolute configuration of the bridgehead carbon atom in bicyclic ß-lactams to the sign of the 220 nm band observed in their electronic circular dichroism (ECD) spectra is examined for ring-expanded cephalosporin analogues. To this end, a series of model compounds with a seven-membered ring condensed with the ß-lactam unit was synthesized. A key step of their synthesis was either the ring-closing metathesis (RCM) or the free radical cyclization leading to the seven-membered ring with an S, O, or C atom at the 6 position in the bicyclic skeleton. To investigate the scope and limitations of the simple, empirically established helicity rule, a combination of ECD spectroscopy, variable-temperature ECD measurements, X-ray analysis, and time-dependent density functional theory (TD-DFT) calculations was used. A comparison of the experimental ECD spectra with the spectra simulated by TD-DFT calculations gives a reasonable interpretation of the Cotton effects observed in the 240-215 nm spectral range. The results suggest that the helicity rule does not apply to the investigated compounds because of the planarity of their amide chromophore. Thus, these compounds do not constitute an exception to the rule that was established for bi- and polycyclic ß-lactams with the nonplanar amide chromophore only.