Method and basis set dependence of the NICS indexes of aromaticity for benzene

The role of theory level in prediction of benzene magnetic indexes of aromaticity is analysed and compared with calculated nuclear magnetic shieldings of ³He used as NMR probe. Three closely related nucleus‐independent chemical shift (NICS) based indexes were calculated for benzene at SCF‐HF, MP2, and DFT levels of theory and the impact of basis set on these quantities was studied. The changes of benzene NICS(0), NICS(1), and NICS(1)zz parameters calculated using SCF‐HF, MP2 and several density functionals were within 1 to 3 ppm. Similar deviations between magnetic indexes of aromaticity were observed for values calculated with selected basis sets. Only very small effect of polar solvent on benzene aromaticity was predicted. The ³He nuclear magnetic isotropic shielding (σ) and its zz‐components (σ_zz) of helium atom approaching the centre of benzene ring from above produced similar curves versus benzene‐He distance to NICS parameters calculated for similarly moving Bq ghost atom. We also propose an experimental verification of NICS calculations by designing the ³He NMR measurement for benzene saturated with helium gas or in low temperature matrices.     

Quantum delocalization of benzene in the ring puckering coordinates

The effect of quantum mechanical delocalization of atomic nuclei on the conformation of the six‐membered ring structure in two hydrocarbons, cyclohexane and benzene, is investigated using ab initio path integral approach. A striking feature of benzene species is revealed using ring puckering coordinate representation, which demonstrates that the zero point motion of the heavy atom skeleton dominates over the out‐of‐plane thermal motions of the ring. Even more unexpected is the fact, that this is true not only at low temperature of 150 K, at which such behavior would not be surprising, but also at room temperature, where the nuclear quantum effects are usually of lesser importance, especially in the case of such heavy nuclei as carbon. In view of this finding the planar conformation of benzene, whose equilibrium (T = 0 K) geometry results from the well‐known properties of the electronic structure, can be elucidated also at nonzero temperature. According to our simulations, it appears as a consequence of quantum delocalization of the carbon nuclei rather than a trivial time average over the classical configurations of the puckered ring. This interesting behavior is contrasted with the clearly nonplanar structure of cyclohexane, whose ring puckering states can be unequivocally assigned even if the nuclear delocalization is taken into account. © 2014 Wiley Periodicals, Inc.     

3He NMR studies on helium–pyrrole,helium–indole,and helium–carbazole systems: a new tool for following chemistry of heterocyclic compounds

The ³He nuclear magnetic shieldings were calculated for free helium atom and He–pyrrole, He–indole, and He–carbazole complexes. Several levels of theory, including Hartree–Fock (HF), Second‐order Møller‐Plesset Perturbation Theory (MP2), and Density Functional Theory (DFT) (VSXC, M062X, APFD, BHandHLYP, and mPW1PW91), combined with polarization‐consistent pcS‐2 and aug‐pcS‐2 basis sets were employed. Gauge‐including atomic orbital (GIAO) calculated ³He nuclear magnetic shieldings reproduced accurately previously reported theoretical values for helium gas. ³He nuclear magnetic shieldings and energy changes as result of single helium atom approaching to the five‐membered ring of pyrrole, indole, and carbazole were tested. It was observed that ³He NMR parameters of single helium atom, calculated at various levels of theory (HF, MP2, and DFT) are sensitive to the presence of heteroatomic rings. The helium atom was insensitive to the studied molecules at distances above 5 Å. Our results, obtained with BHandHLYP method, predicted fairly accurately the He–pyrrole plane separation of 3.15 Å (close to 3.24 Å, calculated by MP2) and yielded a sizable ³He NMR chemical shift (about ?1.5 ppm). The changes of calculated nucleus‐independent chemical shifts (NICS) with the distance above the rings showed a very similar pattern to helium‐3 NMR chemical shift. The ring currents above the five‐membered rings were seen by helium magnetic probe to about 5 Å above the ring planes verified by the calculated NICS index. Copyright © 2014 John Wiley & Sons, Ltd.     

3He NMR: from free gas to its encapsulation in fullerene

The ³He nuclear magnetic shieldings were calculated for single helium atom, its dimer, simple models of fullerene cages (He@C_n), and single wall carbon nanotubes. The performances of several levels of theory (HF, MP2, DFT‐VSXC, CCSD, CCSD(T), and CCSDT) were tested. Two sets of polarization‐consistent basis sets were used (pcS‐n and aug‐pcS‐n), and an estimate of ³He nuclear magnetic shieldings in the complete basis set limit using a two‐parameter fit was established. Theoretical ³He results reproduced accurately previously reported theoretical values for helium gas, dimer, and helium probe inside several fullerene cages. Excellent agreement with experimental values was achieved. ³He nuclear magnetic shieldings of single helium atom approaching various points of benzene ring were tested, and an impact of ³He confinement within fullerene cages of different size on the ³He chemical shift was determined. Copyright © 2013 John Wiley & Sons, Ltd.     

Ground- and excited-state aromaticity and antiaromaticity in benzene and cyclobutadiene

The aromaticity and antiaromaticity of the ground state (S 0), lowest triplet state (T 1), and first singlet excited state (S 1) of benzene, and the ground states (S 0), lowest triplet states (T 1), and the first and second singlet excited states (S 1 and S 2) of square and rectangular cyclobutadiene are assessed using various magnetic criteria including nucleus-independent chemical shifts (NICS), proton shieldings, and magnetic susceptibilities calculated using complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). These magnetic criteria strongly suggest that, in contrast to the well-known aromaticity of the S 0 state of benzene, the T 1 and S 1 states of this molecule are antiaromatic. In square cyclobutadiene, which is shown to be considerably more antiaromatic than rectangular cyclobutadiene, the magnetic properties of the T 1 and S 1 states allow these to be classified as aromatic. According to the computed magnetic criteria, the T 1 state of rectangular cyclobutadiene is still aromatic, but the S 1 state is antiaromatic, just as the S 2 state of square cyclobutadiene; the S 2 state of rectangular cyclobutadiene is nonaromatic. The results demonstrate that the well-known "triplet aromaticity" of cyclic conjugated hydrocarbons represents a particular case of a broader concept of excited-state aromaticity and antiaromaticity. It is shown that while electronic excitation may lead to increased nuclear shieldings in certain low-lying electronic states, in general its main effect can be expected to be nuclear deshielding, which can be substantial for heavier nuclei.     

A Nuclear Singlet Lifetime of More than One Hour in Room‐Temperature Solution

Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are supremely important techniques with numerous applications in almost all branches of science. However, until recently, NMR methodology was limited by the time constant T₁ for the decay of nuclear spin magnetization through contact with the thermal molecular environment. Long‐lived states, which are correlated quantum states of multiple nuclei, have decay time constants that may exceed T₁ by large factors. Here we demonstrate a nuclear long‐lived state comprising two ¹³C nuclei with a lifetime exceeding one hour in room‐temperature solution, which is around 50 times longer than T₁. This behavior is well‐predicted by a combination of quantum theory, molecular dynamics, and quantum chemistry. Such ultra‐long‐lived states are expected to be useful for the transport and application of nuclear hyperpolarization, which leads to NMR and MRI signals enhanced by up to five orders of magnitude.     

First-principles calculation of 17O and 25Mg NMR shieldings in MgO at finite temperature: rovibrational effect in solids

The temperature dependence of (17)O and (25)Mg NMR chemical shifts in solid MgO have been calculated using a first-principles approach. Density functional theory, pseudopotentials, a plane-wave basis set, and periodic boundary conditions were used both to describe the motion of the nuclei and to compute the NMR chemical shifts. The chemical shifts were obtained using the gauge-including projector augmented wave method. In a crystalline solid, the temperature dependence is due to both (i) the variation of the averaged equilibrium structure and (ii) the fluctuation of the atoms around this structure. In MgO, the equilibrium structure at each temperature is uniquely defined by the cubic lattice parameters, which we take from experiment. We evaluate the effect of the fluctuations within a quasiharmonic approximation. In particular, the dynamical matrix, defining the harmonic Hamiltonian, has been computed for each equilibrium volume. This harmonic Hamiltonian was used to generate nuclear configurations that obey quantum statistical mechanics. The chemical shifts were averaged over these nuclear configurations. The results reproduce the previously published experimental NMR data measured on MgO between room temperature and 1000 degrees C. It is shown that the chemical shift behavior with temperature cannot be explained by thermal expansion alone. Vibrational corrections due to the fluctuations of atoms around their equilibrium position are crucial to reproduce the experimental results.     

Multiply Borylated Arenes: X‐ray Crystal Structure Analyses and Quantum Chemical Calculations

Optimised synthesis procedures and results of X‐ray single crystal structure analyses for 4‐(dibromoboryl)toluene, 1, 3‐bis(dibromoboryl)benzene, 1, 4‐bis(dibromoboryl)benzene, and 1, 3, 5‐tris(dibromoboryl)benzene are reported. These compounds have also been studied by Hartree‐Fock (HF), density functional theory (DFT), and Mßller‐Plesset second‐order perturbation (MP2) methods in combination with the polarized double‐ζ valence (SVP) and polarized triple‐ζ valence (TZVP) basis sets of Ahlrichs and coworkers. A comparison of the quantum chemical results for optimised geometries and computed NMR chemical shifts with experiment is presented to test the quality of the various methods for this class of compounds. All DFT methods tested yield optimised geometries within the experimental error bars of 3σ for bond lengths, whereas larger deviations among the methods are observed for computed NMR chemical shifts. This calibration recommends the B3LYP/SVP combination as a reliable and computationally efficient level of theory to assess the structures and absolute and relative ¹H‐, ¹³C‐ and ¹¹B NMR shift values of borylated aromatic compounds in future investigations.     

DFT calculation of structures and NMR chemical shifts of simple models of small diameter zigzag single wall carbon nanotubes (SWCNTs)

Linearly conjugated benzene rings (acenes), belt‐shape molecules (cyclic acenes) and model single wall carbon nanotubes (SWCNTs) were fully optimized at the unrestricted level of density functional theory (UB3LYP/6‐31G*). The models of SWCNTs were selected to get some insight into the potential changes of NMR chemical shift upon systematic increase of the molecular size. The theoretical NMR chemical shifts were calculated at the B3LYP/pcS‐2 level of theory using benzene as reference. In addition, the change of radial breathing mode (RBM), empirically correlated with SWCNT diameter, was directly related with the radius of cyclic acenes. Both geometrical and NMR parameters were extrapolated to infinity upon increase in the studied systems size using a simple two‐parameter mathematical formula. Very good agreement between calculated and available experimental CC bond lengths of acenes was observed (RMS of 0.0173 Å). The saturation of changes in CC bond lengths and ¹H and ¹³C NMR parameters for linear and cyclic acenes, starting from 7–8 conjugated benzene rings, was observed. The ¹³C NMR parameters of individual carbon atoms from the middle of ultra‐thin (4,0) SWCNT formed from 10 conjugated cyclic acenes differ by about 130 ppm from the corresponding open end carbon nuclei. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of nuclear quantum effects on hydrogen bonding

The impact of nuclear quantum effects on hydrogen bonding is investigated for a series of hydrogen fluoride (HF)n clusters and a partially solvated fluoride anion, F-(H2O). The nuclear quantum effects are included using the path integral formalism in conjunction with the Car-Parrinello molecular dynamics (PICPMD) method and using the second-order vibrational perturbation theory (VPT2) approach. For the HF clusters, a directional change in the impact of nuclear quantum effects on the hydrogen-bonding strength is observed as the clusters evolve toward the condensed phase. Specifically, the inclusion of nuclear quantum effects increases the F-F distances for the (HF)n=2-4 clusters and decreases the F-F distances for the (HF)n>4 clusters. This directional change occurs because the enhanced electrostatic interactions between the HF monomers become more dominant than the zero point energy effects of librational modes as the size of the HF clusters increases. For the F-(H2O) system, the inclusion of nuclear quantum effects decreases the F-O distance and strengthens the hydrogen bonding interaction between the fluoride anion and the water molecule because of enhanced electrostatic interactions. The vibrationally averaged 19F shielding constant for F-(H2O) is significantly lower than the value for the equilibrium geometry, indicating that the electronic density on the fluorine decreases as a result of the quantum delocalization of the shared hydrogen. Deuteration of this system leads to an increase in the vibrationally averaged F-O distance and nuclear magnetic shielding constant because of the smaller degree of quantum delocalization for deuterium.     

Systematic investigation on the geometric dependence of the calculated nuclear magnetic shielding constants

We perform a systematic examination on the dependence of the calculated nuclear magnetic shielding constants on the chosen geometry for a selective set of density functional methods of B3LYP, PBE0, and OPBE. We find that the OPBE exchange-correlation functional performs remarkably well when either the optimized geometries or the experimental geometries are used. The popular B3LYP and PBE0 functionals have a clear tendency of deshielding, giving shieldings that are usually too low and shifts that are usually too high, at the experimental geometries. Combined with the Hartree-Fock geometries, however, much improved magnetic constants are obtained for B3LYP and PBE0, due to the compensation effect from the systematic underestimation of bond lengths by the Hartree-Fock method.     

Internal proton transfer and H2 rotations in the H5(+) cluster: a marked influence on its thermal equilibrium state

Classical and path integral Monte Carlo (CMC, PIMC) "on the fly" calculations are carried out to investigate anharmonic quantum effects on the thermal equilibrium structure of the H5(+) cluster. The idea to follow in our computations is based on using a combination of the above-mentioned nuclear classical and quantum statistical methods, and first-principles density functional (DFT) electronic structure calculations. The interaction energies are computed within the DFT framework using the B3(H) hybrid functional, specially designed for hydrogen-only systems. The global minimum of the potential is predicted to be a nonplanar configuration of C(2v) symmetry, while the next three low-lying stationary points on the surface correspond to extremely low-energy barriers for the internal proton transfer and to the rotation of the H2 molecules, around the C2 axis of H5(+), connecting the symmetric C(2v) minima in the planar and nonplanar orientations. On the basis of full-dimensional converged PIMC calculations, results on the quantum vibrational zero-point energy (ZPE) and state of H5(+) are reported at a low temperature of 10 K, and the influence of the above-mentioned topological features of the surface on its probability distributions is clearly demonstrated.     

Is the Conventional Interpretation of the Anisotropic Effects of CC Double Bonds and Aromatic Rings in NMR Spectra in Terms of the π‐Electron Shielding/Deshielding Contributions Correct?

Based on the nucleus‐independent chemical shift (NICS) concept, isotropic magnetic shielding values have been computed along the three Cartesian axes for ethene, cyclobutadiene, benzene, naphthalene, and benzocyclobutadiene, starting from the molecular/ring center up to 10 Å away. These through‐space NMR spectroscopic shielding (TSNMRS) values, which reflect the anisotropic effects, have been broken down into contributions from localized‐ and canonical molecular orbitals (LMOs and CMOs); these contributions revealed that the proton NMR spectroscopic chemical shifts of nuclei that are spatially close to the C?C double bond or the aromatic ring should not be explained in terms of the conventionally accepted π‐electron shielding/deshielding effects. In fact, these effects followed the predictions only for the antiaromatic cyclobutadiene ring.     

Are ring currents still useful to rationalize the benzene proton magnetic shielding?

[structure: see text] The conventional interpretation of proton NMR chemical shifts is supported by large basis set ab initio quantum mechanical calculations. The benzene protons are predicted to lie within the deshielding zone defined in terms of the out-of-plane magnetic shielding domain. However, ring currents by themselves are not sufficient to account quantitatively for the observed benzene proton downfield chemical shift. sigma-Electron contributions must also be taken into account. The conventional explanation for the ethyne proton chemical shift is valid.     

Quantum wavepacket ab initio molecular dynamics: generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.     

Geometric dependence of the B3LYP-predicted magnetic shieldings and chemical shifts

We perform a systematic investigation of how the B3LYP/6-311+G(2d,p) calculated 13C nuclear magnetic shielding constants depend on the 6-31G(d)-optimized geometries for a set of 18 molecules with various chemical environments. For absolute shieldings, the Hartree-Fock (HF)-optimized geometries lead to a mean absolute deviation (MAD) of 5.65 ppm, while the BLYP- and B3LYP-optimized geometries give MADs of 13.07 and 10.14 ppm, respectively. For chemical shifts, the HF, BLYP and B3LYP geometries lead to MADs of 2.36, 5.80, and 4.43 ppm, respectively. We find that the deshielding tendency of B3LYP can be effectively compensated by using the HF-optimized geometries. When we apply the B3LYP//HF protocol to versicolorin A and 5alpha-androstan-3,17-dione, MADs of 1.86 and 1.41 ppm, respectively, are obtained for chemical shifts, in satisfactory agreement with the experiment.     

Ab initio quantum dynamical study of the vinylidene-acetylene isomerization

The dynamics of vinylidene-acetylene isomerization has been studied quantum mechanically, based on a new ab initio calculated potential energy surface (PES). The grid underlying the PES and the dynamic treatment rest on planar 4-atom Jacobi-like coordinates. Three degrees of freedom, the C-C bond length and the two Jacobi-like angles are treated explicitly, while the two other coordinates relating to the C-H bond lengths have been optimized in the ab initio treatment. The energies of the resulting 3D grid have been computed with the CCSD(T) method, using a cc-pVTZ basis set, while selected stationary points have been characterized at a higher level of theory. The subsequent dynamic treatment reproduces very satisfactorily the experimental photodetachment spectrum of Lineberger and coworkers. Preliminary results are also reported for the lifetime of vinylidene. Received: 5 June 1998/Accepted: 23 July 1998 / Published online: 9 October 1998     

A coherent state approach to semiclassical nonadiabatic dynamics

A semiclassical (SC) approximation to the quantum mechanical propagator for nonadiabatic systems is derived. Our derivation starts with an exact path integral expression that uses canonical coherent states for the nuclear degrees of freedom and spin coherent states for the electronic degrees of freedom. A stationary path approximation (SPA) is then applied to the path integral to obtain the SC approximation. The SPA results in complex classical trajectories of both nuclear and electronic degrees of freedom and a double ended boundary condition. The root search problem is solved using the previously proposed "real trajectory local search" algorithm. The SC approximation is tested on three simple one dimensional two-state systems proposed by Tully [J. Chem. Phys. 93, 1061 (1990)], and the SC results are compared to Ehrenfest and surface hopping predictions. Excellent agreement with quantum results is reached when the SC trajectory is far away from caustics. We discuss the origin of caustics in this SC formalism and the strengths and weaknesses of this approach.     

Experimental and theoretical IR,Raman, NMR spectra of 2‐, 3‐, and 4‐nitrobenzoic acids

The influence of the position of nitro group toward the carboxylic group on the vibration structure of the molecule was estimated. Optimized geometrical structures were calculated (HF, B3PW91, B3LYP). Experimental and theoretical FT‐IR, FT‐Raman, and nuclear magnetic resonance (NMR) spectra of the title compounds were recorded and analyzed. The most important vibrational bands of nitro and carboxyl groups and the benzene ring were assigned. Wavenumbers and intensities for the three acids studied were compared and discussed. Data of chemical shifts in ¹H and ¹³C NMR spectra of 2‐, 3‐, and 4‐nitrobenzoic acids were analyzed in comparison with benzoic acid molecule. The calculated parameters are compared with experimental characteristics of these molecules. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007