Benchmarking density-functional theory calculations of NMR shielding constants and spin-rotation constants using accurate coupled-cluster calculations

Efficient calculation of nuclear spin-rotation constants from auxiliary density functional theory

The computation of the spin-rotation tensor within the framework of auxiliary density functional theory (ADFT) in combination with the gauge including atomic orbital (GIAO) scheme, to treat the gauge origin problem, is presented. For the spin-rotation tensor, the calculation of the magnetic shielding tensor represents the most demanding computational task. Employing the ADFT-GIAO methodology, the central processing unit time for the magnetic shielding tensor calculation can be dramatically reduced. In this work, the quality of spin-rotation constants obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good and very similar to the ones obtained by the coupled-cluster single-doubles-perturbative triples-GIAO methodology. With the improved computational performance achieved, the computation of the spin-rotation tensors of large systems or along Born-Oppenheimer molecular dynamics trajectories becomes feasible in reasonable times. Three models of carbon fullerenes containing hundreds of atoms and thousands of basis functions are used for benchmarking the performance. Furthermore, a theoretical study of temperature effects on the structure and spin-rotation tensor of the H(12)C-(12)CH-DF complex is presented. Here, the temperature dependency of the spin-rotation tensor of the fluorine nucleus can be used to identify experimentally the so far unknown bent isomer of this complex. To the best of our knowledge this is the first time that temperature effects on the spin-rotation tensor are investigated.

Theoretical gas to liquid shift of (15)N isotropic nuclear magnetic shielding in nitromethane using ab initio molecular dynamics and GIAO/GIPAW calculations

Chemical shift requires the knowledge of both the sample and a reference magnetic shielding. In few cases as nitrogen (15N), the standard experimental reference corresponds to its liquid phase. Theoretical estimate of NMR magnetic shielding parameters of compounds in their liquid phase is then mandatory but usually replaced by an easily-get gas phase value, forbidding direct comparisons with experiments. We propose here to combine ab initio molecular dynamic simulations with the calculations of magnetic shielding using GIAO approach on extracted cluster's structures from MD. Using several computational strategies, we manage to accurately calculate 15N magnetic shielding of nitromethane in its liquid phase. Theoretical comparison between liquid and gas phase allows us to extrapolate an experimental value for the 15N magnetic shielding of nitromethane in gas phase between -121.8 and -120.8 ppm.

Toward Relatively General and Accurate Quantum Chemical Predictions of Solid-State (17)O NMR Chemical Shifts in Various Biologically Relevant Oxygen-Containing Compounds

Oxygen is an important element in most biologically significant molecules, and experimental solid-state (17)O NMR studies have provided numerous useful structural probes to study these systems. However, computational predictions of solid-state (17)O NMR chemical shift tensor properties are still challenging in many cases, and in particular, each of the prior computational works is basically limited to one type of oxygen-containing system. This work provides the first systematic study of the effects of geometry refinement, method, and basis sets for metal and nonmetal elements in both geometry optimization and NMR property calculations of some biologically relevant oxygen-containing compounds with a good variety of XO bonding groups (X = H, C, N, P, and metal). The experimental range studied is of 1455 ppm, a major part of the reported (17)O NMR chemical shifts in organic and organometallic compounds. A number of computational factors toward relatively general and accurate predictions of (17)O NMR chemical shifts were studied to provide helpful and detailed suggestions for future work. For the studied kinds of oxygen-containing compounds, the best computational approach results in a theory-versus-experiment correlation coefficient (R(2)) value of 0.9880 and a mean absolute deviation of 13 ppm (1.9% of the experimental range) for isotropic NMR shifts and an R(2) value of 0.9926 for all shift-tensor properties. These results shall facilitate future computational studies of (17)O NMR chemical shifts in many biologically relevant systems, and the high accuracy may also help the refinement and determination of active-site structures of some oxygen-containing substrate-bound proteins.

Converging nuclear magnetic shielding calculations with respect to basis and system size in protein systems

Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van der Waals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size.

MP2 calculation of (77) Se NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the Second-order Möller-Plesset perturbation theory (MP2) calculation of (77) Se NMR chemical shifts (methods and basis sets, relativistic corrections, and solvent effects) are addressed with a special emphasis on relativistic effects. For the latter, paramagnetic contribution (390-466 ppm) dominates over diamagnetic term (192-198 ppm) resulting in a total shielding relativistic correction of about 230-260 ppm (some 15% of the total values of selenium absolute shielding constants). Diamagnetic term is practically constant, while paramagnetic contribution spans over 70-80 ppm. In the (77) Se NMR chemical shifts scale, relativistic corrections are about 20-30 ppm (some 5% of the total values of selenium chemical shifts). Solvent effects evaluated within the polarizable continuum solvation model are of the same order of magnitude as relativistic corrections (about 5%). For the practical calculations of (77) Se NMR chemical shifts of the medium-sized organoselenium compounds, the most efficient computational protocols employing relativistic Dyall's basis sets and taking into account relativistic and solvent corrections are suggested. The best result is characterized by a mean absolute error of 17 ppm for the span of (77) Se NMR chemical shifts reaching 2500 ppm resulting in a mean absolute percentage error of 0.7%.

The importance of current contributions to shielding constants in density-functional theory

The sources of error in the calculation of nuclear-magnetic-resonance shielding constants determined by density-functional theory are examined.

Calculating nuclear magnetic resonance shieldings using systematic molecular fragmentation by annihilation

Systematic fragmentation accurately predicts theoretical chemical shieldings.

In search of the appropriate theoretically justified mixing coefficient in parameter-free hybrid functionals for computing the NMR parameters

The parameter-free hybrid density functionals, with theoretically justified mixing coefficients, are recommended to predict the NMR parameters.

Alternation of aromatic–nonaromatic rings in belt-like structures. The behavior of [6.8]3cyclacene in magnetic fields

The magnetic response of [6.8]cyclacene suggests a characteristic behavior given by its confinement into a belt-like structure.

Spin-rotation and NMR shielding constants in XF molecules (X = B, Al, Ga, In, and Tl)

Accurate spin-rotation and absolute shielding constants in a series of XF molecules (X = (11)B, (27)Al, (69)Ga, (115)In, and (205)Tl) determined using high-level ab initio coupled-cluster and four-component relativistic density-functional theory (DFT) calculations are presented. The accuracy of the results is established by comparing the relativistically and vibrationally corrected calculated values with available experimental data; for spin-rotation and shielding constants for which no experimental data exist, we provide new and reliable values. For both properties, our results can be considered as reference values against which more approximate quantum-chemical methods can be benchmarked.

New Experimental NMR Shielding Scales Mapped Relativistically from NSR: Theory and Application

The recently proposed relativistic mapping between nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling tensors [J. Chem. Phys. 2013, 138, 134104] is employed to establish new experimental (more precisely, experimentally derived) absolute shielding constants for H and X in HX (X = F, Cl, Br, and I). The results are much more accurate than the old "experimental" values that were based on the well-known nonrelativistic mapping. The relativistic mapping is very robust in the sense that it is rather insensitive to the quality of one-particle basis sets and the treatment of electron correlation. Relativistic effects in the NSR coupling constants are also elucidated in depth.

33S hyperfine interactions in H2S and SO2 and revision of the sulfur nuclear magnetic shielding scale

Using the Lamb-dip technique, the hyperfine structure in the rotational spectra of H2(33)S and (33)SO2 has been resolved and the corresponding parameters--that is, the sulfur quadrupole-coupling and spin-rotation tensors--were determined. The experimental parameters are in good agreement with results from high-level coupled-cluster calculations, provided that up to quadruple excitations are considered in the cluster operator, sufficiently large basis sets are used, and vibrational corrections are accounted for. The (33)S spin-rotation tensor for H2S has been used to establish a new sulfur nuclear magnetic shielding scale, combining the paramagnetic part of the shielding as obtained from the spin-rotation tensor with a calculated value for the diamagnetic part as well as computed vibrational and temperature corrections. The value of 716(5) ppm obtained in this way for the sulfur shielding of H2S is in good agreement with results from high-accuracy quantum-chemical calculations but leads to a shielding scale that is about 28 ppm lower than the one suggested previously in the literature, based on the (33)S spin-rotation constant of OCS.

Halogen effect on structure and 13C NMR chemical shift of 3,6-disubstituted-N-alkyl carbazoles

Structures of selected 3,6-dihalogeno-N-alkyl carbazole derivatives were calculated at the B3LYP/6-311++G(3df,2pd) level of theory, and their (13) C nuclear magnetic resonance (NMR) isotropic shieldings were predicted using density functional theory (DFT). The model compounds contained 9H, N-methyl and N-ethyl derivatives. The relativistic effect of Br and I atoms on nuclear shieldings was modeled using the spin-orbit zeroth-order regular approximation (ZORA) method. Significant heavy atom shielding effects for the carbon atom directly bonded with Br and I were observed (~-10 and ~-30 ppm while the other carbon shifts were practically unaffected). The decreasing electronegativity of the halogen substituent (F, Cl, Br, and I) was reflected in both nonrelativistic and relativistic NMR results as decreased values of chemical shifts of carbon atoms attached to halogen (C3 and C6) leading to a strong sensitivity to halogen atom type at 3 and 6 positions of the carbazole ring. The predicted NMR data correctly reproduce the available experimental data for unsubstituted N-alkylcarbazoles.