Zero-point vibrational effects on proton shieldings: functional-group contributions from ab initio calculations

Theoretical Study of the Isotope Effect in Optical Rotation

In this work, the isotope effect in optical rotation (OR) is examined by exploring structure-property relationships for H → D substitutions in chiral molecules. While electronic effects serve as the dominant source of optical activity, there is a non-negligible contribution from nuclear vibrations, which changes with isotopic substitution. We employ a test set of 50 small organic molecules: three-membered rings with varying heteroatoms (PCl, PH, S, NCl, NH, O, and NBr) and functional groups (Me, F), and simulations were run at the B3LYP/aug-cc-pVDZ level of theory. The objectives of this work are to determine locations of isotopic substitution that result in significant changes in the vibrational correction to the OR and to evaluate which vibrational modes and electronic response are the major contributors to the isotope effect. Molecules with more polarizable heteroatoms in the ring (e.g., S and P) have the largest change in the vibrational correction compared to the unsubstituted parent molecules. In many cases, isotopic substitution made to the hydrogens on the opposite side of the ring from the functional group provides the largest change in the OR. H/D wagging modes and C vibrations (for D-C centers) are the largest contributors to the isotope effect. This is explained with a molecular orbital decomposition analysis of the OR. The relevant vibrational modes affect the orbital transitions that are already significant at the equilibrium geometry. However, this effect is only large when polarizable heteroatoms are involved because the electron density surrounding them is diffuse enough to feel the subtle effect of change in mass due to isotopic substitution on the relevant vibrational modes.

Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods

An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals (LHFs) is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes zero-field splitting (ZFS), hyperfine coupling (HFC), and the g-tensor. For consistency, we calculate these three tensors at the same level of theory, i.e., using scalar-relativistic X2C augmented with spin-orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the HFC constant is large. For small HFC constants, the relative error is often large, and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with a very large ZFS and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows use of large basis sets for converged HFCs. Overall, current-dependent meta-generalized gradient approximations and LHFs show some potential; however, the currently available functionals leave a lot to be desired, and the predictive power is limited.

New pecJ-n (n = 1, 2) Basis Sets for Selenium Atom Purposed for the Calculations of NMR Spin-Spin Coupling Constants Involving Selenium

We present new compact pecJ-n (n = 1, 2) basis sets for the selenium atom developed for the quantum-chemical calculations of NMR spin-spin coupling constants (SSCCs) involving selenium nuclei. These basis sets were obtained at the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) level with the property-energy consistent (PEC) method, which was introduced in our previous papers. The existing SSCC-oriented selenium basis sets are rather large in size, while the PEC method gives more compact basis sets that are capable of providing accuracy comparable to that reached using the property-oriented basis sets of larger sizes generated with a standard even-tempered technique. This is due to the fact that the PEC method is very different in its essence from the even-tempered approaches. It generates new exponents through the total optimization of angular spaces of trial basis sets with respect to the property under consideration and the total molecular energy. New basis sets were tested on the coupled cluster singles and doubles (CCSD) calculations of SSCCs involving selenium in the representative series of molecules, taking into account relativistic, solvent, and vibrational corrections. The comparison with the experiment showed that the accuracy of the results obtained with the pecJ-2 basis set is almost the same as that provided by a significantly larger basis set, aug-cc-pVTZ-J, while that achieved with a very compact pecJ-1 basis set is only slightly inferior to the accuracy provided by the former.

Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H3PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

High Level Electronic Structure Calculation of Molecular Solid-State NMR Shielding Constants

In this work, we present a quantum mechanics/molecular mechanics (QM/MM) approach for the computation of solid-state nuclear magnetic resonance (SS-NMR) shielding constants (SCs) for molecular crystals. Besides applying standard-DFT functionals like GGAs (PBE), meta-GGAs (TPSS), and hybrids (B3LYP), we apply a double-hybrid (DSD-PBEP86) functional as well as MP2, using the domain-based local pair natural orbital (DLPNO) formalism, to calculate the NMR SCs of six amino acid crystals. All the electronic structure methods used exhibit good correlation of the NMR shieldings with respect to experimental chemical shifts for both 1H and 13C. We also find that local electronic structure is much more important than the long-range electrostatic effects for these systems, implying that cluster approaches using all-electron/Gaussian basis set methods might offer great potential for predictive computations of solid-state NMR parameters for organic solids.

A new double-reference correction scheme for accurate and efficient computation of NMR chemical shieldings

Our novel correction procedure yields high-accuracy DFT predictions of absolute NMR shieldings and enables outliers due to relativistic effects or manifestly inadequate modelling of electron correlation to be easily and unambiguously identified.

15N NMR Shifts of Eumelanin Building Blocks in Water: A Combined Quantum Mechanics/Statistical Mechanics Approach

Theoretical results for the magnetic shielding of protonated and unprotonated nitrogens of eumelanin building blocks including monomers, dimers, and tetramers in gas phase and water are presented. The magnetic property in water was determined by carrying out Monte Carlo statistical mechanics sampling combined with quantum mechanics calculations based on the gauge-including atomic orbitals approach. The results show that the environment polarization can have a marked effect on nitrogen magnetic shieldings, especially for the unprotonated nitrogens. Large contrasts of the oligomerization effect on magnetic shielding show a clear distinction between eumelanin building blocks in solution, which could be detected in nuclear magnetic resonance experiments. Calculations for a π-stacked structure defined by the dimer of a tetrameric building block indicate that unprotonated N atoms are significantly deshielded upon π stacking, whereas protonated N atoms are slightly shielded. The results stress the interest of NMR experiments for a better understanding of the eumelanin complex structure.

Calculating nuclear magnetic resonance chemical shifts in solvated systems

The nuclear magnetic resonance (NMR) chemical shift is extremely sensitive to molecular geometry, hydrogen bonding, solvent, temperature, pH, and concentration. Calculated magnetic shielding constants, converted to chemical shifts, can be valuable aids in NMR peak assignment and can also give detailed information about molecular geometry and intermolecular effects. Calculating chemical shifts in solution is complicated by the need to include solvent effects and conformational averaging. Here, we review the current state of NMR chemical shift calculations in solution, beginning with an introduction to the theory of calculating magnetic shielding in general, then covering methods for inclusion of solvent effects and conformational averaging, and finally discussing examples of applications using calculated chemical shifts to gain detailed structural information.

Dimerization of Acetic Acid in the Gas Phase-NMR Experiments and Quantum-Chemical Calculations

Due to the nature of the carboxylic group, acetic acid can serve as both a donor and acceptor of a hydrogen bond. Gaseous acetic acid is known to form cyclic dimers with two strong hydrogen bonds. However, trimeric and various oligomeric structures have also been hypothesized to exist in both the gas and liquid phases of acetic acid. In this work, a combination of gas-phase NMR experiments and advanced computational approaches were employed in order to validate the basic dimerization model of gaseous acetic acid. The gas-phase experiments performed in a glass tube revealed interactions of acetic acid with the glass surface. On the other hand, variable-temperature and variable-pressure NMR parameters obtained for acetic acid in a polymer insert provided thermodynamic parameters that were in excellent agreement with the MP2 (the second order Møller–Plesset perturbation theory) and CCSD(T) (coupled cluster with single, double and perturbative triple excitation) calculations based on the basic dimerization model. A slight disparity between the theoretical dimerization model and the experimental data was revealed only at low temperatures. This observation might indicate the presence of other, entropically disfavored, supramolecular structures at low temperatures.

Computational study of aromaticity, 1H NMR spectra and intermolecular interactions of twisted thia-norhexaphyrin and its multiply annulated polypyrrolic derivatives

The recently synthesized twisted thia-norhexaphyrin and its multiply annulated polypyrrolic derivatives have been studied computationally. Gauge-including magnetically induced current calculations predict a global nonaromatic character of the initial thia-norhexaphyrin due to the highly-twisted conformation of the macrocycle. Upon the oxidation of the thia-norhexaphyrin four multiply annulated polypyrrolic aromatic macrocycles are formed for which the global aromatic character is confirmed in agreement with experimentally measured ¹H NMR spectra. The calculation of the proton chemical shifts for the studied compounds by direct comparison with the tetramethylsilane standard leads to a significant mean absolute error. At the same time a linear regression procedure for the two selected groups of protons (CH and NH protons) provides much better values of calculated chemical shifts and tight correlation with experiment. The separate consideration of NH protons is motivated by the numerous intermolecular hydrogen bonds in which the protons are involved, which induce considerable upfield shifts, leading to a significant underestimation of the corresponding chemical shifts. Such a selected correlation can be used for accurate estimation of proton chemical shifts of the related porphyrinoids. Bader's theory of Atoms in Molecules has been applied for the studied twisted thia-norhexaphyrin and its multiply annulated polypyrrolic derivatives to characterize intramolecular H-bonds and other non-covalent interactions.

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted ¹³ C and ¹ H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for ¹³ C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.

Dihydrogen contacts observed by through-space indirect NMR coupling

"Through-space" indirect spin-spin couplings between hydrogen atoms formally separated by up to 18 covalent bonds have been detected by NMR experiments in model helical molecules. It is demonstrated that this coupling can provide crucial structural information on the molecular conformation in solution. The coupling pathways have been visualised and analysed by computational methods. The conformational dependence of the coupling is explained in terms of orbital interactions.

Method Calibration or Data Fitting?

We investigate by explicit parameter optimization to what extent basis sets of polarized double-ζ quality can introduce compensating errors in five different density functional methods. It is shown that minor changes in the contraction coefficients of the valence functions in the basis sets can have a significant impact and allow different density functional methods to achieve very similar performances. This holds for nuclear magnetic shielding constants and for isomerization energies, barrier heights, and noncovalent interactions. It is furthermore shown that errors due to neglect of vibrational and solvent effects can be absorbed in the combined method and basis set errors. These findings hold for data sets consisting of 50-150 data points. This raises the question of whether the common practice of identifying combinations of density functional methods and basis sets that have a good performance against a selected set of reference data should be considered as data fitting in the combined parameter space spanned by the method and basis set.

Convergence of nuclear magnetic shieldings and one-bond 1 J(11 B1 H) indirect spin-spin coupling constants in small boron molecules

Self-consistent field Hartree-Fock, density functional theory, and coupled-cluster calculations of the nuclear magnetic shielding constants of BH and BH₃ molecules have been conducted to characterize the convergence of individual results obtained with correlation-consistent and polarization-consistent basis sets. The individual ¹¹ B and ¹ H NMR parameters were estimated in the complete basis set limit and compared with benchmark results. Only the KT3 density functional accurately reproduced ¹¹ B shielding in BH molecule.

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 ³ He 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 ³ He 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 ³ He NMR measurement for benzene saturated with helium gas or in low temperature matrices.

Fully Automated Quantum-Chemistry-Based Computation of Spin-Spin-Coupled Nuclear Magnetic Resonance Spectra

We present a composite procedure for the quantum‐chemical computation of spin–spin‐coupled ¹H NMR spectra for general, flexible molecules in solution that is based on four main steps, namely conformer/rotamer ensemble (CRE) generation by the fast tight‐binding method GFN‐xTB and a newly developed search algorithm, computation of the relative free energies and NMR parameters, and solving the spin Hamiltonian. In this way the NMR‐specific nuclear permutation problem is solved, and the correct spin symmetries are obtained. Energies, shielding constants, and spin–spin couplings are computed at state‐of‐the‐art DFT levels with continuum solvation. A few (in)organic and transition‐metal complexes are presented, and very good, unprecedented agreement between the theoretical and experimental spectra was achieved. The approach is routinely applicable to systems with up to 100–150 atoms and may open new avenues for the detailed (conformational) structure elucidation of, for example, natural products or drug molecules.

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data.

Rovibrational and Temperature Effects in Theoretical Studies of NMR Parameters

The demand for high precision calculations of NMR shieldings (or their related values, chemical shifts δ) and spin–spin coupling constants facilitating and supporting detailed interpretations of NMR spectra increases hand in hand with the development of computational techniques and hardware resources. Highly sophisticated calculations including even relativistic effects are nowadays possible for these properties. However, NMR parameters depend not only on molecular structure and environment but also on molecular flexibility and temperature and the apparent success of theoretical predictions for molecular equilibrium geometries creates a demand for zero-point vibrational and temperature corrections. In this chapter we describe briefly the theory behind rovibrational corrections and review then some important contributions to this field.

Theoretical and experimental NMR studies on muscimol from fly agaric mushroom (Amanita muscaria)

In this article we report results of combined theoretical and experimental NMR studies on muscimol, the bioactive alkaloid from fly agaric mushroom (Amanita muscaria). The assignment of (1)H and (13)C NMR spectra of muscimol in DMSO-d6 was supported by additional two-dimensional heteronuclear correlated spectra (2D NMR) and gauge independent atomic orbital (GIAO) NMR calculations using density functional theory (DFT). The effect of solvent in theoretical calculations was included via polarized continuum model (PCM) and the hybrid three-parameter B3LYP density functional in combination with 6-311++G(3df,2pd) basis set enabled calculation of reliable structures of non-ionized (neutral) molecule and its NH and zwitterionic forms in the gas phase, chloroform, DMSO and water. GIAO NMR calculations, using equilibrium and rovibrationally averaged geometry, at B3LYP/6-31G* and B3LYP/aug-cc-pVTZ-J levels of theory provided muscimol nuclear magnetic shieldings. The theoretical proton and carbon chemical shifts were critically compared with experimental NMR spectra measured in DMSO. Our results provide useful information on its structure in solution. We believe that such data could improve the understanding of basic features of muscimol at atomistic level and provide another tool in studies related to GABA analogs.

Theoretical study of the H/D isotope effect on phase transition of hydrogen-bonded organic conductor κ-H3(Cat-EDT-TTF)2

κ-H₃(Cat-EDT-TTF)₂ (H-TTF) is a hydrogen-bonded π-electron system. Only its isotopologue, D-TTF, shows the phase transition. We obtained a symmetric single-well effective-PEC for H-TTF and low-barrier effective-PEC for D-TTF.

Geometries of Third-Row Transition-Metal Complexes from Density-Functional Theory

A set of 41 metal-ligand bond distances in 25 third-row transition-metal complexes, for which precise structural data are known in the gas phase, is used to assess optimized and zero-point averaged geometries obtained from DFT computations with various exchange-correlation functionals and basis sets. For a given functional (except LSDA) Stuttgart-type quasi-relativistic effective core potentials and an all-electron scalar relativistic approach (ZORA) tend to produce very similar geometries. In contrast to the lighter congeners, LSDA affords reasonably accurate geometries of 5d-metal complexes, as it is among the functionals with the lowest mean and standard deviations from experiment. For this set the ranking of some other popular density functionals, ordered according to decreasing standard deviation, is BLYP > VSXC > BP86 ≈ BPW91 ≈ TPSS ≈ B3LYP ≈ PBE > TPSSh > B3PW91 ≈ B3P86 ≈ PBE hybrid. In this case hybrid functionals are superior to their nonhybrid variants. In addition, we have reinvestigated the previous test sets for 3d- (Bühl M.; Kabrede, H. J. Chem. Theory Comput. 2006, 2, 1282-1290) and 4d- (Waller, M. P.; Bühl, M. J. Comput. Chem. 2007, 28, 1531-1537) transition-metal complexes using all-electron scalar relativistic DFT calculations in addition to the published nonrelativistic and ECP results. For this combined test set comprising first-, second-, and third-row metal complexes, B3P86 and PBE hybrid are indicated to perform best. A remarkably consistent standard deviation of around 2 pm in metal-ligand bond distances is achieved over the entire set of d-block elements.

Theoretical analysis of geometry and NMR isotope shift in hydrogen-bonding center of photoactive yellow protein by combination of multicomponent quantum mechanics and ONIOM scheme

Multicomponent quantum mechanical (MC_QM) calculation has been extended with ONIOM (our own N-layered integrated molecular orbital + molecular mechanics) scheme [ONIOM(MC_QM:MM)] to take account of both the nuclear quantum effect and the surrounding environment effect. The authors have demonstrated the first implementation and application of ONIOM(MC_QM:MM) method for the analysis of the geometry and the isotope shift in hydrogen-bonding center of photoactive yellow protein. ONIOM(MC_QM:MM) calculation for a model with deprotonated Arg52 reproduced the elongation of O-H bond of Glu46 observed by neutron diffraction crystallography. Among the unique isotope shifts in different conditions, the model with protonated Arg52 with solvent effect reasonably provided the best agreement with the corresponding experimental values from liquid NMR measurement. Our results implied the availability of ONIOM(MC_QM:MM) to distinguish the local environment around hydrogen bonds in a biomolecule.

Enhancing NMR Prediction for Organic Compounds Using Molecular Dynamics

NMR spectroscopy is a crucial tool in organic chemistry for the routine characterization of small molecules, structural elucidation of natural products, and study of reaction mechanisms. Although there is evidence that thermal motions strongly affect observed resonances, conventional predictions are performed only on stationary structures. Here we show that quasiclassical molecular dynamics provides a highly accurate and broadly applicable method for improving shielding predictions. Gas-phase values of the absolute shieldings of protons and carbons are predicted to nearly within experimental uncertainty, while the chemical shifts of large systems such as natural products are closely reproduced. Importantly, these results are obtained without the use of any empirical corrections. Our analysis suggests that the linear scaling factors currently employed are primarily a correction for vibrational effects. As a result, our method extends the reach of prediction methods to the study of molecules with unusual dynamics such as the iconic and controversial [18]annulene. Our predictions agree closely with experiment at both low and high temperatures and provide strong evidence that the equilibrium structure of [18]annulene is planar and aromatic.

Nonempirical calculations of the one-bond (29)Si-(13)C spin-spin coupling constants taking into account relativistic and solvent corrections

The computational study of the one-bond (29)Si-(13)C spin-spin coupling constants has been performed at the second-order polarization propagator approximation (SOPPA) level in the series of 60 diverse silanes with a special focus on the main factors affecting the accuracy of the calculation including the level of theory, the quality of the basis set, and the contribution of solvent and relativistic effects. Among three SOPPA-based methods, SOPPA(MP2), SOPPA(CC2), and SOPPA(CCSD), the best result was achieved with SOPPA(CCSD) when used in combination with Sauer's basis set aug-cc-pVTZ-J characterized by the mean absolute error of calculated coupling constants against the experiment of ca 2 Hz in the range of ca 200 Hz. The SOPPA(CCSD)/aug-cc-pVTZ-J method is recommended as the most accurate and effective computational scheme for the calculation of (1)J(Si,C). The slightly less accurate but essentially more economical SOPPA(MP2)/aug-cc-pVTZ-J and/or SOPPA(CC2)/aug-cc-pVTZ-J methods are recommended for larger molecular systems. It was shown that solvent and relativistic corrections do not play a major role in the computation of the total values of (1)J(Si,C); however, taking them into account noticeably improves agreement with the experiment. The rovibrational corrections are estimated to be of about 1 Hz or 1-1.5% of the total value of (1)J(Si,C).

One-bond 29Si-1H spin-spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations, relativistic effects, and vibrational corrections

A number of most representative second order polarization propagator approach (SOPPA) based wavefunction methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), and density functional theory (DFT) based methods, B3LYP, PBE0, KT2, and KT3, have been benchmarked in the calculation of the one-bond (29)Si-(1)H spin-spin coupling constants in the series of halosilanes SiH(n)X(4-n) (X = F, Cl, Br, I), both at the non-relativistic and full four-parameter Dirac's relativistic levels taking into account vibrational corrections. At the non-relativistic level, the wavefunction methods showed much better results as compared with those of DFT. At the DFT level, out of four tested functionals, the Perdew, Burke, and Ernzerhof's PBE0 showed best performance. Taking into account, relativistic effects and vibrational corrections noticeably improves wavefunction methods results, but generally worsens DFT results.

Probing isotope shifts in 103Rh and 195Pt NMR spectra with density functional theory

Zero-point vibrationally averaged (rg(0)) structures were computed at the PBE0/SDD/6-31G* level for the [Pt(35)Cln(37)Cl5-n(H2(18)O)](-) (n = 0-5), cis-Pt(35)Cln(37)Cl4-n(H2(18)O)(H2(16)O) (n = 0-4), fac-[Pt(35)Cln(37)Cl3-n(H2(18)O)(H2(16)O)2](+) (n = 0-3), [Pt(35)Cln(37)Cl5-n((16/18)OH)](2-) (n = 0-5), cis-[Pt(35)Cln(37)Cl4-n((16/18)OH)2](2-) (n = 0-4), fac-[Pt(35)Cln(37)Cl3-n((16/18)OH)3](2-) (n = 0-3), cis-[Pt(35)Cln(37)Cl2-n((16/18)OH)4](2-) (n = 0-2), [Pt(35)Cln(37)Cl1-n((16/18)OH)5](2-) (n = 0-1), [Rh(35)Cln(37)Cl5-n(H2O)](2-) (n = 0-5), cis-[Rh(35)Cln(37)Cl4-n(H2O)2](-) (n = 0-4), and fac-Rh(35)Cln(37)Cl3-n(H2O)3 (n = 0-3) isotopologues and isotopomers. Magnetic shielding constants, computed at the ZORA-SO/PW91/QZ4P/TZ2P level, were used to evaluate the corresponding (35/37)Cl isotope shifts on the (195)Pt and (103)Rh NMR spectra, which are known experimentally. While the observed effects are reproduced reasonably well computationally in terms of qualitative trends and the overall order of magnitude (ca. 1 ppm), quantitative agreement with experiment is not yet achieved. Only small changes in M-Cl and M-O bonds upon isotopic substitution, on the order of femtometers, are necessary to produce the observed isotope shifts.

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH2 O, H2 O, HF, F2 , HCN, SiH4 and H2 S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS-2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization-consistent pcS-n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS-2 and aug-cc-pVTZ-J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS-2, MP2/pcS-2 and DFT/CBS calculations with pcS-n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts.

Role of zero-point vibrational corrections to carbon hyperfine coupling constants in organic π radicals

By analyzing a set of organic π radicals, we demonstrate that zero-point vibrational corrections give significant contributions to carbon hyperfine coupling constants, in one case even inducing a sign reversal for the coupling constant. We discuss the implications of these findings for the computational analysis of electron paramagnetic spectra based on hyperfine coupling constants evaluated at the equilibrium geometry of radicals. In particular, we note that a dynamical description that involves the nuclear motion is in many cases necessary in order to achieve a semi-quantitatively predictive theory for carbon hyperfine coupling constants. In addition, we discuss the implications of the strong dependence of the carbon hyperfine coupling constants on the zero-point vibrational corrections for the selection of exchange-correlation functionals in density functional theory studies of these constants.

Molecular structure refinement by direct fitting of atomic coordinates to experimental ESR spectra

An attempt is made to bypass spectral analysis and fit internal coordinates of radicals directly to experimental liquid- and solid-state electron spin resonance (ESR) spectra. We take advantage of the recently introduced large-scale spin dynamics simulation algorithms and of the fact that the accuracy of quantum mechanical calculations of ESR parameters has improved to the point of quantitative correctness. Partial solutions are offered to the local minimum problem in spectral fitting and to the problem of spin interaction parameters (hyperfine couplings, chemical shifts, etc.) being very sensitive to vibrational excursions from the equilibrium geometry.

Vibrational averaging of the chemical shift in crystalline α-glycine

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane-wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born-Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower-frequency vibrational modes. Temperature excitations of the lowest-frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data.