Semiempirical Methods for Molecular Systems in Strong Magnetic Fields

A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, |B | ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, |B | > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.

Hybrid Density Functional Methods Empirically Optimized for the Computation of (13)C and (1)H Chemical Shifts in Chloroform Solution

Two hybrid generalized-gradient approximation density functionals, WC04 and WP04, are optimized for the prediction of (13)C and (1)H chemical shifts, respectively, using a training set of 43 molecules in chloroform solution. Tests on molecules not included in the training set, namely six stereoisomeric methylcyclohexanols and a β-lactam antibiotic, indicate the models to be robust and moreover to provide results more accurate than those from equivalent B3LYP, PBE1, or mPW1PW91 calculations, particularly for the prediction of downfield resonances in nuclear magnetic resonance spectra. However, linear regression of the B3LYP, PBE1, and mPW1PW91 predicted values on the experimental data improves the accuracy of those models so that they are comparable to WC04 and WP04.

A Fast QM/MM (Quantum Mechanical/Molecular Mechanical) Approach to Calculate Nuclear Magnetic Resonance Chemical Shifts for Macromolecules

A fast approach to calculate nuclear magnetic resonance (NMR) chemical shifts within the quantum mechanical/molecular mechanical (QM/MM) framework has been developed. The QM treatment is based on our recently implemented MNDO/NMR method (Wang et al. J. Chem. Phys. 2004, 120, 11392). The effect of the QM/MM partitioning on chemical shifts has been investigated by test calculations on the water dimer and on the protein crambin. It has been shown that the quantum mechanical treatment of the hydrogen bond and nearby groups with significant magnetic susceptibilities is necessary in order to reproduce the full QM results. The method is also applied to a protein-ligand complex FKBP-GPI, and excellent agreement for proton chemical shifts of the ligand is obtained by including the side-chain atoms of the binding site residues into the QM region. The NMR chemical shift calculations using QM/MM-minimized structures still yield satisfactory results. Our results demonstrate that this QM/MM NMR method is able to treat critical regions of very large macromolecules without compromising accuracy if a relatively large QM region is used.

A QUANTUM CHEMISTRY GIAO MOLECULAR SITE APPROACH OF NMR CHEMICAL SHIFTS GENERALIZED TO THE WHOLE PERIODIC TABLE

An accurate and rapid quantum chemistry approach to predicting chemical shifts is applied to 15 N natural abundance NMR spectra of benzothiazoles. This method is of interest in the study of toxic contaminants of biological media. A GIAO approach is used to calculate the nuclear shielding tensor in a perturbational scheme. Similar methods had previously been used for both ab initio and semi-empirical calculations programmed in Gaussian and MOPAC respectively but atomic orbitals specific to molecular sites are shown to improve accuracy in the present work. Some molecular sites are defined in order to polarize the molecular orbitals in the presence of the solvent interactions. For convenience, the extensions are carried out in an independent NMR module designed to work with the MOPAC package and the present application is generalized to the third row elements for the first time. This new theoretical work is described. The application to 15 N chemical shifts for benzothiazoles led to results within 0.5 ppm of values measured in this work. Structural investigations were carried out using the Gaussian98 suite of programs at the DFT B3LYP level of calculation over an extended basis set. These studies show the single chemical shift for benzothiazoles could be the result of rapid tautomeric equilibria. Further investigations show that solvent interactions involving hydrogen bonds should also be taken into account.

Calculating accurate proton chemical shifts of organic molecules with density functional methods and modest basis sets

The purpose of this paper is to convince practitioners of (1)H NMR spectroscopy to consider simple quantum chemical calculations as a viable option to aid them in the assignment of their spectra. To this end, it is demonstrated, on a test set of 80 conformationally stable molecules of various kinds carrying different functional groups, that, in contrast to what is claimed in the literature, large basis sets are not needed to obtain rather accurate predictions of (1)H NMR chemical shifts by quantum chemical calculations. On the other hand, modeling the solvent by an SCRF-type calculation may improve certain predictions significantly. The best accuracy/cost ratio is provided by GIAO calculations in chloroform as a solvent with the specially parametrized WP04 functional of Cramer et al. using the cc-pVDZ or 6-31G** basis set, closely followed by similar calculations with the ubiquitious B3LYP functional (both predict (1)H chemical shifts with an average deviation of ca. 0.12 ppm, if the results are scaled linearly). A slightly higher accuracy can be attained by adding diffuse functions to the basis set, but going to the triple-zeta basis sets which have invariably been used hitherto in calculations of chemical shifts does not lead to any improvement. The popular increment schemes such as those implemented in the ChemDraw or ACD programs do not do nearly as well and are often incapable of correctly distinguishing stereoisomers.

MNDO parameters for the prediction of 19F NMR chemical shifts in biologically relevant compounds

The semiempirical MNDO methodology for qualitative description NMR chemical shifts has now been extended with the addition of NMR-specific parameters for the fluorine atom. This approach can be employed using semiempirical (AM1/PM3) geometries with good accuracy and can be executed at a fraction of the cost of ab initio and DFT methods, providing an attractive option for the computational studies of (19)F NMR for much larger systems. The data set used in the parametrization is large and diverse and specifically geared toward biologically relevant compounds. The new parameters are applicable to fluorine atoms involved in carbon-fluorine bonds. These parameters yield results comparable to NMR calculations performed at the DFT (B3LYP) level using the 6-31++G(d,p) basis set. The average R (2) and rms error for this data set is 0.94 and 13.85 ppm, respectively, compared to 0.96 and 10.45 ppm when DFT methods are used.

Fast semiempirical calculations for nuclear magnetic resonance chemical shifts: a divide-and-conquer approach

A new approach to calculate nuclear magnetic resonance chemical shifts has been implemented at the semiempirical modified neglect of diatomic overlap level using gauge-including atomic orbitals. The perturbed density matrix with respect to the magnetic field is obtained by the diagonalization of the complex Fock matrix using the divide and conquer (DC) method, instead of by solving the computationally expensive coupled perturbed Hartree-Fock equations. Adopting the Patchkovskii and Thiel parameters [S. Patchkovskii and W. Thiel J. Comput. Chem. 20, 1220 (1999)], we were able to reproduce their results for small organic molecules. The errors introduced by DC method are negligible, as shown by the calculations on a series of polyalaine structures. Test calculations on proteins have demonstrated that our approach makes it possible to calculate chemical shifts routinely on systems with hundreds of atoms with good accuracy.

Pose scoring by NMR

Recently, we have developed a fast approach to calculate NMR chemical shifts using the divide and conquer method at the semiempirical level. To demonstrate the utility of this approach for characterizing protein-ligand interactions, we used the deviation of calculated chemical shift perturbations from experiment to determine the orientation of a ligand (GPI-1046) in the binding pocket of the FK506 binding protein (FKBP12). Moreover, we were able to select the native state of the ligand from a collection of decoy poses. A key hydrogen bond between O1 and HN in Ile56 was also identified. Our results suggest that ligand-induced chemical shift perturbations can be used to refine protein/ligand structures.

Backbone structure confirmation and side chain conformation refinement of a bradykinin mimic BKM-824 by comparing calculated (1)H, (13)C and (19)F chemical shifts with experiment

Calculated and experimental (1)H, (13)C and (19)F chemical shifts were compared in BKM-824, a cyclic bradykinin antagonist mimic, c[Ava(1)-Igl(2)-Ser(3)-DF5F(4)-Oic(5)-Arg(6)] (Ava=5-aminovaleric acid, Igl=alpha-(2-indanyl)glycine, DF5F=pentafluorophenylalanine, Oic=(2S,3aS,7aS)-octahydroindole-2-carboxylic acid). The conformation of BKM-824 has been studied earlier by NMR spectroscopy (M. Miskolzie et al., J. Biomolec. Struct. Dyn. 17, 947-955 (2000)). All NMR structures have qualitatively the same backbone structure but there is considerable variation in the side chain conformations. We have carried out quantum mechanical optimization for three representative NMR structures at the B3LYP/6-31G* level, constraining the backbone dihedral angles at their NMR structure values, followed by NMR chemical shift calculations at the optimized structures with the 6-311G** basis set. There is an intramolecular hydrogen bond at Ser(3) in the optimized structures. The experimental (13)C chemical shifts at five C(alpha) positions as well as at the Cbeta, Cgamma and Cdelta position of Ava(1), which forms part of the backbone, are well reproduced by the calculations, confirming the NMR backbone structure. A comparison between the calculated and experimental H(beta) chemical shifts in Igl(2) shows that the dominant conformation at this residue is gauche. Changes of proton chemical shifts with the scan of the chi(1) angle in DF5F(4) suggest that chi(1)180 degrees. The calculated (1)H and (13)C chemical shifts are in good agreement with experiment at the rigid residue Oic(5). None of the models gives accurate results for Arg(6), presumably because of its positive charge. Our study indicates that calculated NMR shifts can be used as additional constraints in conjunction with NMR data to determine protein conformations. However, to be computationally effective, a database of chemical shifts in small peptide fragments should be precalculated.

Evaluation of a (1)h-(13)c NMR spectral library

A simple database of (13)C/(1)H-(13)C spectral lists for 11 673 natural products was created in standard commercial database format. Over 50% of the spectra were predicted using HOSE code descriptors derived from the 50% of spectra having experimental values. Prediction errors obtained by prediction of and comparison to the experimental spectra revealed an exponentially decaying dependence between the average absolute error and the depth of the matching HOSE codes. A subset of the library containing over 1000 (1)H-(13)C assigned experimental spectral lists were used to test against eight alternate query data sets. These sets represent query data from various combinations of 1D-(13)C, 1D-DEPT, and 2D-(1)H-(13)C spectra. Simulated query lists were generated using Monte Carlo methods. As expected, queries based on 2D-(1)H-(13)C data were more likely to find the correct match under unfavorable conditions.