Toward coupled-cluster accuracy in the prediction of nuclear shielding constants: a simple and efficient DFT approach

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.

Absolute 13C Nuclear Magnetic Shielding of Simple Isolated Molecules from Gas Phase Measurements

The new experimental value of 13C absolute shielding constant in an isolated 13CO molecule was evaluated from the 13C and 3He gas phase NMR measurements performed for 3He/13CO mixtures. The...

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.

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%.

Calculation of chemical shift anisotropy in proteins

Individual peptide groups in proteins must exhibit some variation in the chemical shift anisotropy (CSA) of their constituent atoms, but not much is known about the extent or origins of this dispersion. Direct spectroscopic measurement of CSA remains technically challenging, and theoretical methods can help to overcome these limitations by estimating shielding tensors for arbitrary structures. Here we use an automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach to compute (15)N, (13)C' and (1)H chemical shift tensors for human ubiquitin and the GB1 and GB3 fragments of staphylococcal protein G. The average and range of variation of the anisotropies is in good agreement with experimental estimates from solid-state NMR, and the variation among residues is somewhat smaller than that estimated from solution-state measurements. Hydrogen-bond effects account for much of the variation, both between helix and sheet regions, and within elements of secondary structure, but other effects (including variations in torsion angles) may play a role as well.

On Occupied-orbital Dependent Exchange-correlation Functionals: From Local Hybrids to Becke’s B05 Model

Recent work in the field of occupied-orbital dependent (OOD) exchange-correlation functionals in density functional theory is reviewed. The main emphasis is put on the development of so-called local hybrid functionals, and on the nontrivial self-consistent implementation of complex OOD functionals. Local hybrids employ a so-called local mixing function (LMF) to govern their position-dependent exact-exchange admixture. Recently proposed LMFs have provided local hybrids of remarkable accuracy in the computation of thermochemical data and classical reaction barriers, and with good performance for some magnetic-resonance parameters. These local hybrids mix only local and exact exchange and exhibit very few semi-empirical parameters. Further refinement and the efficient implementation of local hybrids offers the prospect of a new level of accuracy in Kohn-Sham density functional calculations. Two levels of the self-consistent implementation of OOD functional are discussed: one may either stop after the derivation of the functional derivatives with respect to the orbitals (FDOs), leading to nonlocal potentials. This is discussed for local hybrids and for general OOD functionals up to and including the complicated B05 real-space model of nondynamical correlation. Alternatively, one may append an additional transformation to local and multiplicative potentials based on the optimized effective potential (OEP) approach or of approximations to the OEP. Numerical results for various properties are reviewed briefly, ranging from nonself-consistent energies via FDO-based calculations to OEP-transformed potentials.

Theoretical analysis of solvent effects on nitrogen NMR chemical shifts in oxazoles and oxadiazoles

Using quantum chemistry methods we have evaluated the solvent effects on the (14)N NMR chemical shifts in five oxa- and oxadiazoles dissolved in twelve solvents. These solvents differ in their polarity with the dielectric constants varying from 2 to 80. Moreover, three of them have a hydrogen-bond donor character. All possible hydrogen-bonding in the water solution with the oxygen and nitrogen (hydrogen-acceptor) centers in oxazoles (2) and oxadiazoles (3) have been considered in our studies. It has been shown that both the pure solvent and hydrogen-bonding effects are significant and result in (14)N magnetic shielding increase. In water solutions the pure solvent effect is larger than the hydrogen-bonding effect. In addition, the solvent effect has been analyzed in terms of its direct and indirect contributions. It should be emphasized that our theoretical results for (14)N chemical shifts in oxa- and oxadiazoles remain in a very good agreement with the accurate experimental data.

Prediction of water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) using correlation-consistent and polarization-consistent basis sets in the Kohn-Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) in the Kohn-Sham (KS) complete basis set (CBS) limit. Correlation-consistent cc-pVxZ and cc-pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ-pVxZ, unc-ccJ-pVxZ, and aug-cc-pVTZ-J) and polarization-consistent pc-n and pcJ-n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT-predicted isotropic shieldings, spin-spin values, and the experimental values was good and similar for the modified correlation-consistent and polarization-consistent basis sets. The BHandH method predicted the most accurate (1)H, (17)O isotropic shieldings and (1)J(OH) coupling constant (deviations from experiment of about -0.2 and -1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and (1)J(OH) is similar to the more advanced methods, second-order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit.

Secondary Structures of Peptides and Proteins via NMR Chemical-Shielding Anisotropy (CSA) Parameters

Complete nuclear magnetic resonance (NMR) chemical-shielding tensors, sigma, have been computed at different levels of density-functional theory (DFT), within the gauge-including atomic orbital (GIAO) formalism, for the atoms of the peptide model For-L-Ala-NH2 as a function of the backbone dihedral angles phi and psi by employing a dense grid of 10 degrees. A complete set of rigorously orthogonal symmetric tensor invariants, {sigma iso, rho, tau}, is introduced, where sigma iso is the usual isotropic chemical shielding, while the newly introduced rho and tau parameters describe the magnitude and the orientation/shape of the chemical-shielding anisotropy (CSA), respectively. The set {sigma iso, rho, tau} is unaffected by unitary transformations of the symmetric part of the shielding tensor. The mathematically and physically motivated {rho, tau} anisotropy pair is easily connected to more traditional shielding anisotropy measures, like span (Omega) and skew (kappa). The effectiveness of the different partitions of the CSA information in predicting conformations of peptides and proteins has been tested throughout the Ramachandran space by generating theoretical NMR anisotropy surfaces for our For-L-Ala-NH2 model. The CSA surfaces, including Omega(phi, psi), kappa(phi, psi), rho(phi, psi), and tau(phi, psi) are highly structured. Individually, none of these surfaces is able to distinguish unequivocally between the alpha-helix and beta-strand secondary structural types of proteins. However, two- and three-dimensional correlated plots, including Omega versus kappa, rho versus tau, and sigma iso versus rho versus tau, especially for 13Calpha, have considerable promise in distinguishing among all four of the major secondary structural elements.

A semiempirical generalized gradient approximation exchange-correlation functional

We describe our attempts to improve upon the quality of the KT1 and KT2 generalized gradient approximation (GGA) exchange-correlation functionals [T. W. Keal and D. J. Tozer, J. Chem. Phys. 119, 3015 (2003)], through the introduction of additional gradient-corrected exchange and correlation terms. A GGA functional, denoted KT3, is presented, which maintains the high quality main-group nuclear magnetic resonance shielding constants obtained with KT1 and KT2; results are 2-3 times more accurate than conventional GGA and hybrid functionals. For the extensive range of systems considered in this study, KT3 also provides atomization energies, ionization potentials, electron affinities, proton affinities, bond angles, and electronic polarizabilities that are comparable to, or that surpass, those of the best present-day GGAs. Furthermore, it provides equilibrium molecular bond lengths and diatomic harmonic vibrational wave numbers that are as accurate as those from the best hybrid functionals. Further improvements are required in the description of classical chemical reaction barriers.

Comparison of density functionals for energy and structural differences between the high- [5T2g:(t2g)4(eg)2] and low- [1A1g:(t2g)6(eg)0] spin states of iron(II) coordination compounds. II. More functionals and the hexaminoferrous cation, [Fe(NH3)6]2+

The ability of different density functionals to describe the structural and energy differences between the high- [(5)T(2g):(t(2g))(4)(e(g))(2)] and low- [(1)A(1g):(t(2g))(6)(e(g))(0)] spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, [Fe(H(2)O)(6)](2+), [J. Chem. Phys. 120, 9473 (2004)] to include a second compound-namely, the hexaminoferrous cation, [Fe(NH(3))(6)](2+)-and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations (GGAs) known as HCTH and the meta-GGA VSXC [which together we refer to as highly parametrized density functionals (HPDFs)], now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from second-order perturbation theory-corrected complete active space self-consistent field (CASPT2) calculations, with spectroscopy oriented configuration interaction (SORCI) calculations, and with ligand field theory (LFT) estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic low-spin-high-spin energy difference, DeltaE(LH) (adia), of 12 000-13 000 cm(-1) for [Fe(H(2)O)(6)](2+) and 9 000-11 000 cm(-1) for [Fe(NH(3))(6)](2+). All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, DeltaE(LH) (adia), is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the low-spin state with respect to the high-spin state. This "density functional theory (DFT) spin pairing-energy problem" persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates DeltaE(LH) (adia) by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Norskov gives good results for DeltaE(LH) (adia) as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairing-energy problem, destabilizing the low-spin state relative to the high-spin state. Best agreement is found for the hybrid functional PBE0.

Density-functional generalized-gradient and hybrid calculations of electromagnetic properties using Slater basis sets

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.

Phosphorus magnetic shielding tensors for transition-metal compounds containing phosphine, phosphido, and phosphinidene ligands: Insights from computational chemistry

The present study examines the quality of the restricted Hartree–Fock (RHF) ab initio, B3LYP hybrid density functional theory (DFT), and relativistic zeroth-order regular approximation (ZORA) DFT methods for the calculation of phosphorus chemical shift (CS) tensors in phosphine, phosphido, and phosphinidene transition-metal complexes. A detailed comparison of calculated and experimental 31P CS tensors allows us to identify the characteristic advantages of each computational method. The results from B3LYP and ZORA-DFT calculations indicate that a double-ζ quality basis set reproduces experimental values of the principal components of the 31P CS tensor in many of the phosphorus-containing transition-metal complexes investigated, whereas the RHF method requires a triple-ζ doubly polarized basis set, yet fails in the case of the terminal phosphido group. Inclusion of the spin-orbit relativistic correction with the ZORA-DFT formalism requires a triple-ζ quality basis set to reproduce the experimental data. We demonstrate the merit of modern computational methods for investigating theoretically the effect of geometric variations upon the phosphorus CS tensor by systematically altering the W—P bond length and the W-P-CMe bond angle in W(CO)5(PMe3). Additionally, a previously reported correlation, determined experimentally, relating the 31P CS tensor to the Fe-P-Fe bond angle in a series of iron phosphido-bridging compounds, has been reproduced with calculations using the model compound Fe2(CO)6(µ2-PPh2)(µ2-Cl). The results presented demonstrate the value of modern computational techniques for obtaining a greater understanding of the relationship between phosphorus chemical shifts and molecular structure.Key words: 31P chemical shift, phosphine, phosphido, phosphinidene, RHF, B3LYP, relativistic, ZORA-DFT.