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Climate change is a critical issue that strongly affects the mental state of many people and often manifests itself as so-called eco-anxiety. Eco-anxiety is mainly evoked by media reporting, as they are the main source of information about climate change. In this study, the aim was to investigate whether there is a difference in the impact of three different media types (video, radio, and newspaper) on an individual’s eco-anxiety level. By conducting a diary study in which participants received climate change-related media input at fixed intervals, the following key findings can be reported: There is a difference between eco-anxiety before and after the media intervention. The video intervention is shown to affect its participants' eco-anxiety. The other media interventions showed no effect. A correlation with neuroticism could be identified, as there is a significant influence on the pre-media intervention level of eco-anxiety and on the overall change in eco-anxiety.

The local vibrational mode analysis developed by Konkoli and Cremer has been successfully applied to characterize the intrinsic bond strength via local bond stretching force constants in molecular systems. A wealth of new insights into covalent bonding and weak chemical interactions ranging from hydrogen, halogen, pnicogen, and chalcogen to tetrel bonding has been obtained. In this work we extend the local vibrational mode analysis to periodic systems, i.e. crystals, allowing for the first time a quantitative in situ measure of bond strength in the extended systems of one, two, and three dimensions. We present the study of one-dimensional polyacetylene and hydrogen fluoride chains and two-dimensional layers of graphene, water, and melamine-cyanurate as well as three-dimensional ice I

The Bacillus subtilis chorismate mutase catalysed Claisen rearrangement of chorismate to prephenate is one of the few pericyclic processes in biology, and as such provides a rare opportunity for un...

Utilizing the analytic derivative formalism for the Mossbauer isomer shift in connection with the Dirac-exact two-component Normalized Elimination of the Small Component (2c-NESC) method a new appr...

Boranes and carboranes form non-classical H-bonds with the π-face of an arene provided entropic factors are excluded, for example via a suitably designed template. The self-assembled Ir-dithiolene phosphine complexes of the type [Cp∗Ir(PR3)S2C2B10H10] (R = C6H4X, X = H, F, OMe) provide such a template. Steric crowding causes that one of the B-H bonds of the carborane is positioned above the phenyl plane of R to form a non-classical B-H…π hydrogen bond. For the gas phase, this is predicted by quantum chemical calculations of the local B-H…π stretching force constants. The solid-state structures of six [Cp∗Ir(PR3)S2C2B10H10] complexes synthesized are in close agreement with the quantum chemical predictions thus suggesting the existence of B-H…π hydrogen bonds. The 1H[11B] NMR titration experiments reveal that non-covalent B-H…π bonds also exists in solution. Calculations show that the bond strength order of the B-H…π H-bond determined with the help of the local stretching force constant is 0.35, comparable to what is found for the H-bond in the water dimer. However, the B-H…π H-bond is electrostatic in nature as confirmed by the topological analysis of the electron density ρ(r). The role of this H-bond in carborane supramolecular chemistry is elucidated and discussed.

A set of 50 molecules with NF bonds was investigated to determine the factors that influence the strength of a NF bond, with the aim of designing a new class of fluorinating agents. The intrinsic bond strength of the NF bonds was used as bond strength measure, derived from local stretching NF force constants obtained at the CCSD(T)/aug-cc-pVTZ and ωB97XD/aug-cc-pVTZ levels of theory. The investigation showed that the NF bond is a tunable covalent bond, with bond strength orders ranging from 2.5 (very strong) to 0.1 (very weak). NF bond strengthening is caused by a combination of different factors and can be achieved by e.g. ionization. Whereas, the NF bond weakening can be achieved by hypervalency on the N atom, using a N→Ch (Ch: O, S, Se) donor-acceptor type bond with different electron-withdrawing groups. These new insights into the nature of the NF bond were used to propose and design a new class of fluorinating agents. Hypervalent amine-chalcogenides turned out as most promising candidates for efficient electrophilic fluorinating agents.

The unified reaction valley approach (URVA) combined with the local mode, ring puckering and electron density analysis is applied to elucidate the mechanistic differences of the non-catalys...

A diverse set of 100 chalcogen-bonded complexes comprising neutral, cationic, anionic, divalent, and double bonded chalcogens has been investigated using ωB97X-D/aug-cc-pVTZ to determine geometries, binding energies, electron and energy density distributions, difference density distributions, vibrational frequencies, local stretching force constants, and associated bond strength orders. The accuracy of ωB97X-D was accessed by CCSD(T)/aug-cc-pVTZ calculations of a subset of 12 complexes and by the CCSD(T)/aug-cc-pVTZ //ωB97X-D binding energies of 95 complexes. Most of the weak chalcogen bonds can be rationalized on the basis of electrostatic contributions, but as the bond becomes stronger, covalent contributions can assume a primary role in the strength and geometry of the complexes. Covalency in chalcogen bonds involves the charge transfer from a lone pair orbital of a Lewis base into the σ* orbital of a divalent chalcogen or a π* orbital of a double bonded chalcogen. We describe for the first time a symmetric chalcogen-bonded homodimer stabilized by a charge transfer from a lone pair orbital into a π* orbital. New polymeric materials based on chalcogen bonds should take advantage of the extra stabilization granted by multiple chalcogen bonds, as is shown for 1,2,5-telluradiazole dimers.

Utilizing all-electron Dirac-exact relativistic calculations with the Normalized Elimination of the Small Component (NESC) method and the local vibrational mode approach, the transition from metal-halide to metal halogen bonding is determined for Au-complexes interacting with halogen-donors. The local stretching force constants of the metal-halogen interactions reveal a smooth transition from weak non-covalent halogen bonding to non-classical 3-center-4-electron bonding and finally covalent metal-halide bonding. The strongest halogen bonds are found for dialkylaurates interacting with Cl 2 or FCl. Differing trends in the intrinsic halogen-metal bond strength, the binding energy, and the electrostatic potential are explained.

The stability of small Aum (m = 4–7) clusters is investigated by analyzing their energetic, geometric, vibrational, magnetic, and electron density properties. Gold clusters can be constructed from stable cyclic 3-center-2-electron (3c-2e) Au3+ units (3-rings) with σ-aromaticity. The stabilization requires a flow of negative charge from internal 3-rings with electron-deficient bonding to peripheral 3-ring units with stronger Au–Au bonds. The valence-isoelectronic clusters Au6 and Au5Zn+ have similar electronic properties: Au5Zn+ is a strongly σ-aromatic molecule. An understanding of the structure of Aum clusters is obtained by deriving a Clar’s Rule equivalent for polycyclic gold clusters: The structure with the larger number of rings with dominant 3c-2e character and a smaller degree of 3c-3e character occupies the global minimum of the Aum potential energy surface.

It is essential to understand the intrinsic stability of the gold-thiolate clusters, which present extensive potential applications in many fields such as the catalysis, biomedicines and molecular machines. The electronic structures and aromaticity indexes of a series of Aum(SH)n (m, n = 5–12) were comprehensively investigated through energetic, vibrational, magnetic, and electronic density properties, which are highly sensitive to the size and topological structure of the cluster. Generally, computational results of energy gap between the frontier molecular orbitals, normalized atomization energy (NAE), and electron localization function (ELF)-σ values exhibit the odd-even effect, in which clusters with the even number of free valence electrons, being reflected by the value of (m–n), possess relatively higher stability than the odd one. However, it is difficult to describe the stability of cluster with the sophisticated three-dimensional structure through one single aromaticity index such as the nucleus-independent chemical shift (NICS) value. Principal component analysis and clustering analysis of the calculation results of Aum(SR)n clusters suggest that the value of (m–n) and the Au4 unit are important for predicting the stability of the Au clusters.

The properties of liquid water are intimately related to the H-bond network among the individual water molecules. Utilizing vibrational spectroscopy and modeling water with DFT-optimized water clusters (6-mers and 50-mers), 16 out of a possible 36 different types of H-bonds are identified and ordered according to their intrinsic strength. The strongest H-bonds are obtained as a result of a concerted push–pull effect of four peripheral water molecules, which polarize the electron density in a way that supports charge transfer and partial covalent character of the targeted H-bond. For water molecules with tetra- and pentacoordinated O atoms, H-bonding is often associated with a geometrically unfavorable positioning of the acceptor lone pair and donor σ*(OH) orbitals so that electrostatic rather than covalent interactions increasingly dominate H-bonding. There is a striking linear dependence between the intrinsic strength of H-bonding as measured by the local H-bond stretching force constant and the delocali...

A total of 202 halogen-bonded complexes have been studied using a dual-level approach: ωB97XD/aug-cc-pVTZ was used to determine geometries, natural bond order charges, charge transfer, dipole moments, electron and energy density distributions, vibrational frequencies, local stretching force constants, and relative bond strength orders n. The accuracy of these calculations was checked for a subset of complexes at the CCSD(T)/aug-cc-pVTZ level of theory. Apart from this, all binding energies were verified at the CCSD(T) level. A total of 10 different electronic effects have been identified that contribute to halogen bonding and explain the variation in its intrinsic strength. Strong halogen bonds are found for systems with three-center-four-electron (3c-4e) bonding such as chlorine donors in interaction with substituted phosphines. If halogen bonding is supported by hydrogen bonding, genuine 3c-4e bonding can be realized. Perfluorinated diiodobenzenes form relatively strong halogen bonds with alkylamines as they gain stability due to increased electrostatic interactions.

The reaction mechanism of the cycloaddition of 10 1,3-dipoles with the two dipolarphiles ethene and acetylene is investigated and compared using the Unified Reaction Valley Approach in a new form, which is based on a dual-level strategy, an accurate description of the reaction valley far out into the van der Waals region, and a comparative analysis of the electronic properties of the reaction complex. A detailed one-to-one comparison of 20 different 1,3-dipolar cycloadditions is performed, and unknown mechanistic features are revealed. There are significant differences in the reaction mechanisms for the two dipolarophiles that result from the van der Waals complex formation in the entrance channel of the cycloadditions. Hydrogen bonding between the 1,3-dipoles and acetylene is generally stronger, which leads to higher reaction barriers in the acetylene case, but which also facilitates to overcome the problem of a reduced charge transfer from 1,3-dipole to acetylene. Mechanistic differences are found in the prechemical and chemical reaction regions with regard to reactant orientation, preparation for the reaction, charge transfer, charge polarization, rehybridization, and bond formation. It is shown that similarities in the reaction barriers as determined by CCSD(T)-F12/aug-cc-pVTZ calculations result from a fortuitous cancellation of different electronic effects. In general, a caveat must be made with regard to oversimplified descriptions of the reaction mechanism based on orbital theory or energy decomposition schemes.

The LUMO of the pnicogen-bonded fluoro-phosphine dimer has PP bonding character. Radical anion and dianion form relatively strong pnicogen bonds with some covalent character where however the dianion turns out to be a second order transition state. The binding energy of ( FPH 2 ) 2 - is 30.4 kcal/mol (CCSD(T)/aug-cc-pVTZ; CASPT2(5,8): 30.7 kcal/mol) and the bond strength order measured with the local PP bond stretching force constant increases from 0.055 for the neutral dimer to 0.187 thus revealing that the stabilization of the radical anion is to a large extend a result of one-electron six-center delocalization. Pnicogen-bonded complexes have a stabilizing electron affinity.

Vibrational frequencies can be measured and calculated with high precision. Therefore, they are excellent tools for analyzing the electronic structure of a molecule. In this connection, the properties of the local vibrational modes of a molecule are best suited. A new procedure is described, which utilizes local CC stretching force constants to derive an aromaticity index (AI) that quantitatively determines the degree of π-delocalization in a cyclic conjugated system. Using Kekulé benzene as a suitable reference, the AIs of 30 mono- and polycyclic conjugated hydrocarbons are calculated. The AI turns out to describe π-delocalization in a balanced way by correctly describing local aromatic units, peripheral, and all-bond delocalization. When comparing the AI with the harmonic oscillator model of AI, the latter is found to exaggerate the antiaromaticity of true and potential 4n π-systems or to wrongly describe local aromaticity. This is a result of a failure of the Badger relationship (the shorter bond is always the stronger bond), which is only a rule and therefore cannot be expected to lead to an accurate description of the bond strength via the bond length. The AI confirms Clar's rule of disjoint benzene units in many cases, but corrects it in those cases where peripheral π-delocalization leads to higher stability. [5]-, [6]-, [7]-Circulene and Kekulene are found to be aromatic systems with varying degree of delocalization. Properties of the local vibrational modes provide an accurate description of π-delocalization and an accurate AI.

β-Hydride eliminations for ethylgold(III) dichloride complexes are identified as reactions with an unusually long prechemical stage corresponding to the conformational preparation of the reaction complex and spanning six phases. The prechemical process is characterized by a geared rotation of the L-Au-L group (L = Cl) driving methyl group rotation and causing a repositioning of the ligands. This requires more than 28 kcal/mol of the total barrier of 34.0 kcal/mol, according to the unified reaction valley approach, which also determines that the energy requirements of the actual chemical process leading to the β-elimination product are only about 5.5 kcal/mol. A detailed mechanistic analysis was used as a basis for a rational design of substrates (via substituents on the ethyl group) and/or ligands, which can significantly reduce the reaction barrier. This strategy takes advantage of either a higher trans activity of the ligands or a tuned electronic demand of the ethyl group. The β-hydride elimination of gold(I) was found to suffer from strong Coulomb and exchange repulsion when a positively charged hydrogen atom enforces a coordination position in a d(10)-configured gold atom, thus triggering an unassisted σ-π Au(I)-C conversion.

The unified reaction valley approach (URVA) used for a detailed mechanistic analysis of chemical reactions is improved in three different ways: (i) Direction and curvature of path are analyzed in terms of internal coordinate components that no longer depend on local vibrational modes. In this way, the path analysis is no longer sensitive to path instabilities associated with the occurrences of imaginary frequencies. (ii) The use of third order terms of the energy for a local description of the reaction valley allows an extension of the URVA analysis into the pre- and postchemical regions of the reaction path, which are typically characterized by flat energy regions. (iii) Configurational and conformational processes of the reaction complex are made transparent even in cases where these imply energy changes far less than a kcal/mol by exploiting the topology of the potential energy surface. As examples, the rhodium-catalyzed methanol carbonization, the Diels-Alder reaction between 1,3-butadiene and ethene, and the rearrangement of HCN to CNH are discussed.

36 halogen-bonded complexes YX⋯ARm (X: F, Cl, Br; Y: donor group; ARm acceptor group) have been investigated at the CCSD(T)/aug-cc-pVTZ level of theory. Binding energies, geometries, NBO charges, charge transfer, dipole moments, electrostatic potential, electron and energy density distributions, difference density distributions, vibrational frequencies, local stretching and bending force constants, and relative bond strength orders n have been calculated and used to order the halogen bonds according to their intrinsic strength. Halogen bonding is found to arise from electrostatic and strong covalent contributions. It can be strengthened by H-bonding or lone pair delocalization. The covalent character of a halogen bond increases in the way 3c-4e (three-center-four-electron) bonding becomes possible. One can characterize halogen bonds by their percentage of 3c-4e bonding. FCl–phosphine complexes can form relatively strong halogen bonds provided electronegative substituents increase the covalent contributions in form of 3c-4e halogen bonding. Binding energies between 1 and 45 kcal mol−1 are calculated, which reflects the large variety in halogen bonding.

The local vibrational mode analysis, originally introduced by Konkoli and Cremer, provides a physically sound platform for a comprehensive analysis of calculated or measured vibrational spectra and for providing detailed insights into chemical bonding and other structural features. In this work, we summarize the essentials of the local vibrational mode theory with a focus on local vibrational force constants and their relationship with compliance and relaxed force constants. Furthermore, we discuss how local vibrational force constants can be used (i) to assess the quality of empirically derived force constants, (ii) to disclose bonding features in large molecules, and (iii) to provide metal ligand force field parameters. Future applications will be suggested.

Normal vibrational modes are generally delocalized over the molecular system, which makes it difficult to assign certain vibrations to specific fragments or functional groups. We introduce a new approach, the Generalized Subsystem Vibrational Analysis (GSVA), to extract the intrinsic fragmental vibrations of any fragment/subsystem from the whole system via the evaluation of the corresponding effective Hessian matrix. The retention of the curvature information with regard to the potential energy surface for the effective Hessian matrix endows our approach with a concrete physical basis and enables the normal vibrational modes of different molecular systems to be legitimately comparable. Furthermore, the intrinsic fragmental vibrations act as a new link between the Konkoli–Cremer local vibrational modes and the normal vibrational modes.

A set of 42 molecules with N-F, O-F, N-Cl, P-F, and As-F bonds has been investigated in the search for potential bond anomalies, which lead to reverse bond length-bond strength (BLBS) relationships. The intrinsic strength of each bond investigated has been determined by the local stretching force constant obtained at the CCSD(T)/aug-cc-pVTZ level of theory. N-F or O-F bond anomalies were found for fluoro amine radicals, fluoro amines, and fluoro oxides, respectively. A rationale for the deviation from the normal Badger-type inverse BLBS relation is given and it is shown that electron withdrawal accompanied by strong orbital contraction and bond shortening is one of the prerequisites for a bond anomaly. In the case of short electron-rich bonds such as N-F or O-F, anomeric delocalization of lone pair electrons in connection with lone pair repulsion are decisive whether a bond anomaly can be observed. This is quantitatively assessed with the help of the CCSD(T) local stretching force constants, CCSD(T) charge distributions, and G4 bond dissociation energies. Bond anomalies are not found for fluoro phosphines and fluoro arsines because the bond weakening effects are no longer decisive.

A novel approach is presented to assess chemical similarity based the local vibrational mode analysis developed by Konkoli and Cremer. The local mode frequency shifts are introduced as similarity descriptors that are sensitive to any electronic structure change. In this work, 59 different monosubstituted benzenes are compared. For a subset of 43 compounds, for which experimental data was available, the ortho-/para- and meta-directing effect in electrophilic aromatic substitution reactions could be correctly reproduced, proving the robustness of the new similarity index. For the remaining 16 compounds, the directing effect was predicted. The new approach is broadly applicable to all compounds for which either experimental or calculated vibrational frequency information is available.

The stability of small Au

A new method for calculating nuclear magnetic resonance shielding constants of relativistic atoms based on the two-component (2c), spin-orbit coupling including Dirac-exact NESC (Normalized Elimination of the Small Component) approach is developed where each term of the diamagnetic and paramagnetic contribution to the isotropic shielding constant σiso is expressed in terms of analytical energy derivatives with regard to the magnetic field B and the nuclear magnetic moment 𝝁. The picture change caused by renormalization of the wave function is correctly described. 2c-NESC/HF (Hartree-Fock) results for the σiso values of 13 atoms with a closed shell ground state reveal a deviation from 4c-DHF (Dirac-HF) values by 0.01%–0.76%. Since the 2-electron part is effectively calculated using a modified screened nuclear shielding approach, the calculation is efficient and based on a series of matrix manipulations scaling with (2M)3 (M: number of basis functions).

The catalytic activity of transition metal complexes (R)nM–L can be predicted utilizing the metal–ligand electronic parameter (MLEP) that is based on the local stretching force constant of the M-L bond. Vibrational spectroscopy is an excellent tool to accurately determine vibrational mode properties such as stretching frequencies. These correspond, because of mode–mode coupling, to delocalized vibrational modes, which have to be first converted into local vibrational modes, and their properties. Each bond of a molecule can be uniquely characterized by the local stretching force constant and frequency. The former is ideally suited to set up a scale of bond strength orders, which identifies weak M–L bonds with promising catalytic activity. It is shown how the MLEP replaces the TEP (Tolman Electronic Parameter), which is based on the CO stretching frequencies of a (CO)nM–L complex and which is now exclusively used in hundreds of investigations. However, the TEP is at best a qualitative parameter that suffers from relatively large mode–mode coupling errors and the basic deficiency of most indirect descriptors: They cannot correctly describe the intrinsic M–L bond strength via the CO stretching frequencies.

A set of 36 pnicogen homo- and heterodimers, R3E···ER3 and R3E···E′R′3, involving differently substituted group Va elements E = N, P, and As has been investigated at the ωB97X-D/aug-cc-pVTZ level of theory to determine the strength of the pnicogen bond with the help of the local E···E′ stretching force constants k(a). The latter are directly related to the amount of charge transferred from an E donor lone pair orbital to an E′ acceptor σ* orbital, in the sense of a through-space anomeric effect. This leads to a buildup of electron density in the intermonomer region and a distinct pnicogen bond strength order quantitatively assessed via k(a). However, the complex binding energy ΔE depends only partly on the pnicogen bond strength as H,E-attractions, H-bonding, dipole-dipole, or multipole-multipole attractions also contribute to the stability of pnicogen bonded dimers. A variation from through-space anomeric to second order hyperonjugative, and skewed π,π interactions is observed. Charge transfer into a π* substituent orbital of the acceptor increases the absolute value of ΔE by electrostatic effects but has a smaller impact on the pnicogen bond strength. A set of 10 dimers obtains its stability from covalent pnicogen bonding whereas all other dimers are stabilized by electrostatic interactions. The latter are quantified by the magnitude of the local intermonomer bending force constants XE···E′. Analysis of the frontier orbitals of monomer and dimer in connection with the investigation of electron difference densities, and atomic charges lead to a simple rationalization of the various facets of pnicogen bonding. The temperature at which a given dimer is observable under experimental conditions is provided.

The nature of the E⋯E′ pnicogen bond (E = N, P, As) in dimers such as H2FP⋯PH2F (1) and H3N⋯PHNO2 (2) can be described using vibrational spectroscopy in form of the calculated infrared and depolarized Raman scattering spectra. Utilizing the six calculated intermonomer frequencies, the corresponding local mode E⋯E′ stretching frequency and force constant are obtained, where the latter provides a unique measure of the E⋯E′ bond strength. Pnicogen bonding in 1 is relative strong (bond strength order n = 0.151) and covalent whereas pnicogen bonding in 2 is electrostatic (n = 0.047) because of a different bonding mechanism.

The conformational landscape and ring-puckering properties of e-caprolactone have been analyzed by using microwave spectroscopy and quantum chemical calcula- tions. Two conformers were detected in a supersonic jet ex- pansion, the most stable form being a chair containing the ester group in its rectangular flap. This conformation bene- fits from reduced CH2 bond eclipsing and angle strain, while p-electron delocalization in the ester group is increased. The derived effective structure of the chair form satisfactorily agrees with the calculated near-equilibrium structure. A twist-boat conformer was also identified (9.4 kJ mol � 1 higher in energy at CCSD(T)/aug-cc-pVTZ level), and was located in the boat-twist-boat pseudorotation cycle of the seven-mem- bered ring. Three other low-energy conformers were investi- gated and characterized in terms of the four puckering coor- dinates of the seven-membered ring. Potential interconver- sions in the four-dimensional conformation space are also discussed.

CX (X = F, Cl, Br, I) and CE bonding (E = O, S, Se, Te) was investigated for a test set of 168 molecules using the local CX and CE stretching force constants k(a) calculated at the M06-2X/cc-pVTZ level of theory. The stretching force constants were used to derive a relative bond strength order (RBSO) parameter n. As alternative bond strength descriptors, bond dissociation energies (BDE) were calculated at the G3 level or at the two-component NESC (normalized elimination of the small component)/CCSD(T) level of theory for molecules with X = Br, I or E = Se, Te. RBSO values reveal that both bond lengths and BDE values are less useful when a quantification of the bond strength is needed. CX double bonds can be realized for Br- or I-substituted carbenium ions where as suitable reference the double bond of the corresponding formaldehyde homologue is used. A triple bond cannot be realized in this way as the diatomic CX(+) ions with a limited π-donor capacity for X are just double-bonded. The stability of halonium ions increases with the atomic number of X, which is reflected by a strengthening of the fractional (electron-deficient) CX bonds. An additional stability increase of up to 25 kcal/mol (X = I) is obtained when the X(+) ion can form a bridged halonium ion with ethene such that a more efficient 2-electron-3-center bonding situation is created.

The carbon—halogen and carbon—chalcogen bonding of 84 molecules was investigated utilizing local vibrational modes calculated at the M06-2X/cc-pVTZ level of theory including anharmonicity corrections in all cases. The relative bond strength order of each CX or CE bond (X = F, Cl; E = O, S) was derived from the local CX or CE stretching force constant and compared with trends of calculated bond lengths r and bond dissociation energies (BDE) obtained at the G3 level of theory. It is shown that both bond length r and BDE are not reliable bond strength descriptors. The CX double bond is realized for some Cl-substituted carbenium ions, however, not for the corresponding F-derivatives. Diatomic CF+ and CCl+ possess fully developed double bonds but not, as suggested in the literature, triple bonds. Halonium ions have fractional (electron-deficient) CX bonds, which can be stabilized by σ-donor substituents or by an increased polarizability of the halogen atom as with Cl. Bridged halonium ions are more stable than their acyclic counterparts, which results from more effective two-electron-three-center bonding. © 2014 Wiley Periodicals, Inc.

Dirac-exact relativistic methods, i.e., 2- or 1-component methods which exactly reproduce the one-electron energies of the original 4-component Dirac method, have established a standard for reliable relativistic quantum chemical calculations targeting medium- and large-sized molecules. Their development was initiated and facilitated in the late 1990s by Dyall's development of the normalized elimination of the small component (NESC). Dyall's work has fostered the conversion of NESC and related (later developed) methods into routinely used, multipurpose Dirac-exact methods by which energies, first-order, and second-order properties can be calculated at computational costs, which are only slightly higher than those of nonrelativistic methods. This review summarizes the development of a generally applicable 1-component NESC algorithm leading to the calculation of reliable energies, geometries, electron density distributions, electric moments, electric field gradients, hyperfine structure constants, contact densities and Mossbauer isomer shifts, nuclear quadrupole coupling constants, vibrational frequencies, infrared intensities, and static electric dipole polarizabilities. In addition, the derivation and computational possibilities of 2-component NESC methods are discussed and their use for the calculation of spin-orbit coupling (SOC) effects in connection with spin-orbit splittings and SOC-corrected energies are demonstrated. The impact of scalar relativistic and spin-orbit effects on molecular properties is presented. WIREs Comput Mol Sci 2014, 4:436–467. Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

The normalized elimination of the small component (NESC) method is a first principles 2-component relativistic approach that leads to the Dirac-exact description of one-electron systems. It is a powerful method to routinely investigate chemical and physical properties of molecules containing relativistic atoms. The vibrational modes of mercury halides are investigated to derive via the corresponding local HgX (X = H, F, Cl, Br, I, At) stretching modes an appropriate measure for the HgX bond strength. It is shown that HgF bonding in HgF4 is stronger than that in HgF2, which is a result of enhanced charge transfer from Hg to the four F atoms and the formation of electron deficient 2e-4c bonds with strong ionic character. A generally applicable bonding model for HgX molecules is outlined. The relativistic counterpart of the Schrodinger equation is the Dirac equation (14, 15), which provides the basis for an exact description of a single electron in an external field. The step from a single electron to a multiple electron problem requires relativistic calculations both for the one-electron and the two-electron part of the Hamiltonian. The quantum mechanical methodology to reliably calculate molecular properties of molecules containing relativistic atoms developed much slower than its non-relativistic counterpart. In the last 15 years, the Dirac-exact relativistic methods have been developed, which lead to accurate 4-component results with a 2-component or even 1-component approach. The first Dirac-exact relativistic 2-component method was developed by Dyall (16) in form of the normalized elimination of the small component (NESC) approach. Dyall developed the NESC method at a time when most quantum chemists followed an operator-driven strategy to convert Dirac's four-component description by a series of transformations into a two-component one. Contrary to these attempts, he attacked the problem by starting from a matrix formulation of the Dirac equation and then carried out all the pertinent transformations by adhering to the matrix

Enediynes undergo a Bergman cyclization reaction to form the labile 1,4-didehy-drobenzene (p-benzyne) biradical. The energetics of this reaction and the related Schreiner–Pascal reaction as well as that of the Myers–Saito and Schmittel reactions of enyne-allenes are discussed on the basis of a variety of quantum chemical and available experimental results. The computational investigation of enediynes has been beneficial for both experimentalists and theoreticians because it has led to new synthetic challenges and new computational methodologies. The accurate description of biradicals has been one of the results of this mutual fertilization. Other results have been the computer-assisted drug design of new antitumor antibiotics based on the biological activity of natural enediynes, the investigation of hetero- and metallo-enediynes, the use of enediynes in chemical synthesis and materials science, or an understanding of catalyzed enediyne reactions. For further resources related to this article, please visit the WIREs website.

Increasing the effective electronegativity of two atoms forming a triple bond can increase the strength of the latter. The strongest bonds found in chemistry involve protonated species of hydrogen cyanide, carbon monoxide, and dinitrogen. CCSD(T)/CBS (complete basis set) and G4 calculations reveal that bond dissociation energies are misleading strength descriptors. The strength of the bond is assessed via the local stretching force constants, which suggest relative bond strength orders (RBSO) between 2.9 and 3.4 for heavy atom bonding (relative to the CO bond strength in methanol (RBSO = 1) and formaldehyde (RBSO = 2)) in [HCNH](+)((1)Σ(+)), [HCO](+)((1)Σ(+)), [HNN](+)((1)Σ(+)), and [HNNH](2+)((1)Σg(+)). The increase in strength is caused by protonation, which increases the electronegativity of the heavy atom and thereby decreases the energy of the bonding AB orbitals (A, B: C, N, O). A similar effect can be achieved by ionization of a nonbonding or antibonding electron in CO or NO. The strongest bond with a RBSO value of 3.38 is found for [HNNH](2+) using scaled CCSD(T)/CBS frequencies determined for CCSD(T)/CBS geometries. Less strong is the NN bond in [FNNH](2+) and [FNNF](2+).

The 24 normal and 24 local vibrational modes of the formic acid dimer formed by two trans formic acid monomers to a ring (TT1) are analysed utilising preferentially experimental frequencies, but also CCSD(T)/CBS and ωB97X-D harmonic vibrational frequencies. The local hydrogen bond (HB) stretching frequencies are at 676 cm−1 and by this 482 and 412 cm−1 higher compared to the measured symmetric and asymmetric HB stretching frequencies at 264 and 194 cm−1. The adiabatic connection scheme between local and normal vibrational modes reveals that the lowering is due to the topology of dimer TT1, mass coupling, and avoided crossings involving the H⋅⋅⋅OC bending modes. The HB local mode stretching force constant is related to the strength of the HB whereas the normal mode stretching force constant and frequency lead to an erroneous underestimation of the HB strength. The HB in TT1 is stabilised by electron delocalisation in the O=C–O units fostered by forming a ring via double HBs. This implies that the CO apart ...

A new method, dubbed "HAXIS" is introduced to describe local and global shape properties of a protein helix via its axis. HAXIS is based on coarse-graining and spline-fitting of the helix backbone. At each Cα anchor point of the backbone, a Frenet frame is calculated, which directly provides the local vector presentation of the helix. After cubic spline-fitting of the axis line, its curvature and torsion are calculated. This makes a rapid comparison of different helix forms and the determination of helix similarity possible. Distortions of the helix caused by individual residues are projected onto the helix axis and presented either by the rise parameter per residue or by the local curvature of the axis. From a non-redundant set of 2,017 proteins, 15,068 helices were investigated in this way. Helix start and helix end as well as bending and kinking of the helix are accurately described. The global properties of the helix are assessed by a polynomial fit of the helix axis and the determination of its overall curving and twisting. Long helices are more regular shaped and linear whereas short helices are often strongly bent and twisted. The distribution of different helix forms as a function of helix length is analyzed.

Chiral discrimination of homochiral and heterochiral H-bonded complexes is a challenge for both experimentalists and computational chemists. It is demonstrated that a two-pronged approach based on far-infrared vibrational spectroscopy and the calculation of local mode frequencies facilitates the chiral discrimination of H-bonded dimers. The local H-bond stretching frequencies identify the strongest H-bonds and by this the dominating chiral diastereomer. This is shown in the case of peroxide, trioxide, hydrazine, glycidol, and butan-2-ol dimers as well as propylene oxide…glycidol complexes investigated with the help of second-order Moller–Plesset perturbation, coupled cluster, and density functional theory calculations where, in the latter case, the ωB97X-D functional was used for an improved description of H-bonding. In some cases, additional intermolecular interactions overrule the important role of H-bonding, which is found by calculating chirodiastaltic energies. Chirality 25:185–196, 2013. © 2013 Wiley Periodicals, Inc.

Configuration interaction (CI) theory has dominated the first 50 years of quantum chemistry before it was replaced by many-body perturbation theory and coupled cluster theory. However, even today it plays an important role in the education of everybody who wants to enter the realm of quantum chemistry. Apart from this, full CI is the method of choice for getting exact energies for a given basis set. The development of CI theory from the early days of quantum chemistry up to our time is described with special emphasis on the size-extensivity problem, which after its discovery has reduced the use of CI methods considerably. It led to the development of the quadratic CI (QCI) approach as a special form of size-extensive CI. Intimately linked with QCI is the scientific dispute between QCI developers and their opponents, who argued that the QCI approach in its original form does not lead to a set of size-extensive CI methods. This dispute was settled when it was shown that QCI in its original form can be converted into a generally defined series of size-extensive methods, which however have to be viewed as a series of simplified coupled cluster methods rather than a series of size-extensive CI methods. © 2013 John Wiley & Sons, Ltd.

The analytical energy gradient and Hessian of the two-component Normalized Elimination of the Small Component (2c-NESC) method with regard to the components of the electric field are derived and used to calculate spin-orbit coupling (SOC) corrected dipole moments and dipole polarizabilities of molecules, which contain elements with high atomic number. Calculated 2c-NESC dipole moments and isotropic polarizabilities agree well with the corresponding four-component-Dirac Hartree–Fock or density functional theory values. SOC corrections for the electrical properties are in general small, but become relevant for the accurate prediction of these properties when the molecules in question contain sixth and/or seventh period elements (e.g., the SO effect for At2 is about 10% of the 2c-NESC polarizability). The 2c-NESC changes in the electric molecular properties are rationalized in terms of spin-orbit splitting and SOC-induced mixing of frontier orbitals with the same j = l + s quantum numbers.

For the first time, nonclassical hydrogen (H)-bonding involving a B-H···π interaction is described utilizing both quantum chemical predictions and experimental realization. In the gas phase, a B-H···π H-bond is observed in either B2H6···benzene (ΔE = -5.07 kcal/mol) or carborane···benzene (ΔE = -3.94 kcal/mol) complex at reduced temperatures. Ir-dimercapto-carborane complexes [Cp*Ir(S2C2B10H10)] are designed to react with phosphines PR3 (R = C6H4X, X = H, F, OMe) to give [Cp*Ir(PR3)S2C2B10H10] for an investigation of B-H···π interactions at ambient temperatures. X-ray diffraction studies reveal that the interaction between the carborane BH bonds and the phosphine aryl substituents involves a BH···π H-bond (H···π distance: 2.40-2.76 Å). (1)H NMR experiments reveal that B-H···π interactions exist in solution according to measured (1)H{(11)B} signals at ambient temperatures in the range 0.0 ≤ δ ≤ 0.3 ppm. These are high-field shifted by more than 1.5 ppm relative to the (1)H{(11)B} signals obtained for the PMe3 analog without B-H···π bonding. Quantum chemical calculations suggest that the interaction is electrostatic and the local (B)H···ring stretching force constant is as large as the H-bond stretching force constant in the water dimer.

The Tolman electronic parameter (TEP) derived from the A1-symmetrical CO stretching frequency of nickel-tricarbonyl complexes L-Ni(CO)3 with varying ligands L is misleading as (i) it is not based on a mode decoupled CO stretching frequency and (ii) a generally applicable and quantitatively correct or at least qualitatively reasonable relationship between the TEP and the metal-ligand bond strength does not exist. This is shown for a set of 181 nickel-tricarbonyl complexes using both experimental and calculated TEP values. Even the use of mode-mode decoupled CO stretching frequencies (L(ocal)TEPs) does not lead to a reliable description of the metal-ligand bond strength. This is obtained by introducing a new electronic parameter that is directly based on the metal-ligand local stretching force constant. For the test set of 181 nickel complexes, a direct metal-ligand electronic parameter (MLEP) in the form of a bond strength order is derived, which reveals that phosphines and related ligands (amines, arsines, stibines, bismuthines) are bonded to Ni both by σ-donation and π-back-donation. The strongest Ni-L bonds are identified for carbenes and cationic ligands. The new MLEP quantitatively assesses electronic and steric factors.