Nuclei-selected NMR shielding calculations: A sublinear-scaling quantum-chemical method

Analytical Second-Order Properties for the Random Phase Approximation: Nuclear Magnetic Resonance Shieldings

A method for the analytical computation of nuclear magnetic resonance (NMR) shieldings within the direct random phase approximation (RPA) is presented. As a starting point, we use the RPA ground-state energy expression within the resolution-of-the-identity approximation in the atomic-orbital formalism. As has been shown in a recent benchmark study using numerical second derivatives [Glasbrenner, M. J. Chem. Theory Comput. 2022, 18, 192], RPA based on a Hartree-Fock reference shows accuracies comparable to coupled cluster singles and doubles (CCSD) for NMR chemical shieldings. Together with the much lower computational cost of RPA, it has emerged as an accurate method for the computation of NMR shieldings. Therefore, we aim to extend the applicability of RPA NMR to larger systems by introducing analytical second-order derivatives, making it a viable method for the accurate and efficient computation of NMR chemical shieldings.

Efficient low-scaling computation of NMR shieldings at the second-order Møller-Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric

A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller-Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller-Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved. In addition, the method uses the resolution-of-the-identity approximation with an attenuated Coulomb metric and Cholesky decomposition of pseudo-density matrices. The sparsity in the three-center integrals is exploited with sparse linear algebra approaches, leading to reduced computational cost and memory demands. Test calculations show that the deviations from NMR shifts obtained with canonical MP2 are small if appropriate thresholds are used. The performance of the method is illustrated in calculations on DNA strands and on glycine chains with up to 283 atoms and 2864 basis functions.

Benchmarking the Accuracy of the Direct Random Phase Approximation and σ-Functionals for NMR Shieldings

A method for computing NMR shieldings with the direct random phase approximation (RPA) and the closely related σ-functionals [Trushin, E.; Thierbach, A.; Görling, A. Toward chemical accuracy at low computational cost: density functional theory with σ-functionals for the correlation energy. J. Chem. Phys. 2021, 154, 014104] is presented, which is based on a finite-difference approach. The accuracy is evaluated in benchmark calculations using high-quality coupled cluster values as a reference. Our results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree-Fock exchange in the functional. NMR shieldings computed with direct RPA using a Hartree-Fock reference are significantly more accurate than MP2 shieldings and comparable to CCSD shieldings. Also, the basis set convergence is analyzed and it is shown that at least triple-zeta basis sets are required for reliable results.

Spatial Contributions to Nuclear Magnetic Shieldings

We develop a methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities which are calculated from the current density via the Biot-Savart relation. Atomic contributions to nuclear magnetic shielding constants can be estimated within our framework with a Becke partitioning scheme. The new features have been implemented in the GIMIC program and are applied in this work to the study of the 1H and 13C nuclear magnetic shieldings in benzene (C6H6) and cyclobutadiene (C4H4). The new methodology allows a visual inspection of the spatial origins of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constant of a single nucleus, something which has not been hitherto easily accomplished. Analysis of the shielding densities shows that diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions, as the shielding or deshielding is determined by the direction of the current-density flux with respect to the studied nucleus instead of the tropicity. Becke partitioning of the magnetic shieldings shows that the magnetic shielding contributions mainly originate from the studied atom and its nearest neighbors, confirming the localized character of nuclear magnetic shieldings.

Automated fragmentation quantum mechanical calculation of 13C and 1H chemical shifts in molecular crystals

In this work, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach was applied to calculate the ¹³C and ¹H nuclear magnetic resonance (NMR) chemical shifts in molecular crystals. Two benchmark sets of molecular crystals were selected to calculate the NMR chemical shifts. Systematic investigation was conducted to examine the convergence of AF-QM/MM calculations and the impact of various density functionals with different basis sets on the NMR chemical shift prediction. The result demonstrates that the calculated NMR chemical shifts are close to convergence when the distance threshold for the QM region is larger than 3.5 Å. For ¹³C chemical shift calculations, the mPW1PW91 functional is the best density functional among the functionals chosen in this study (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB98, and OPBE), while the OB98 functional is more suitable for the ¹H NMR chemical shift prediction of molecular crystals. Moreover, with the B3LYP functional, at least a triple-ζ basis set should be utilized to accurately reproduce the experimental ¹³C and ¹H chemical shifts. The employment of diffuse basis functions will further improve the accuracy for ¹³C chemical shift calculations, but not for the ¹H chemical shift prediction. We further proposed a fragmentation scheme of dividing the central molecule into smaller fragments. By comparing with the results of the fragmentation scheme using the entire central molecule as the core region, the AF-QM/MM calculations with the fragmented central molecule can not only achieve accurate results but also reduce the computational cost. Therefore, the AF-QM/MM approach is capable of predicting the ¹³C and ¹H NMR chemical shifts for molecular crystals accurately and effectively, and could be utilized for dealing with more complex periodic systems such as macromolecular polymers and biomacromolecules. The AF-QM/MM program for molecular crystals is available at https://github.com/shiman1995/NMR.

Computation of NMR Shielding Constants for Solids Using an Embedded Cluster Approach with DFT, Double-Hybrid DFT, and MP2

In this work, we explore the accuracy of post-Hartree–Fock (HF) methods and double-hybrid density functional theory (DFT) for the computation of solid-state NMR chemical shifts. We apply an embedded cluster approach and investigate the convergence with cluster size and embedding for a series of inorganic solids with long-range electrostatic interactions. In a systematic study, we discuss the cluster design, the embedding procedure, and basis set convergence using gauge-including atomic orbital (GIAO) NMR calculations at the DFT and MP2 levels of theory. We demonstrate that the accuracy obtained for the prediction of NMR chemical shifts, which can be achieved for molecular systems, can be carried over to solid systems. An appropriate embedded cluster approach allows one to apply methods beyond standard DFT even for systems for which long-range electrostatic effects are important. We find that an embedded cluster should include at least one sphere of explicit neighbors around the nuclei of interest, given that a sufficiently large point charge and boundary effective potential embedding is applied. Using the pcSseg-3 basis set and GIAOs for the computation of nuclear shielding constants, accuracies of 1.6 ppm for ⁷Li, 1.5 ppm for ²³Na, and 5.1 ppm for ³⁹K as well as 9.3 ppm for ¹⁹F, 6.5 ppm for ³⁵Cl, 7.4 ppm for ⁷⁹Br, and 7.5 ppm for ²⁵Mg as well as 3.8 ppm for ⁶⁷Zn can be achieved with MP2. Comparing various DFT functionals with HF and MP2, we report the superior quality of results for methods that include post-HF correlation like MP2 and double-hybrid DFT.

Predicting 19 F NMR Chemical Shifts: A Combined Computational and Experimental Study of a Trypanosomal Oxidoreductase-Inhibitor Complex

The absence of fluorine from most biomolecules renders it an excellent probe for NMR spectroscopy to monitor inhibitor-protein interactions. However, predicting the binding mode of a fluorinated ligand from a chemical shift (or vice versa) has been challenging due to the high electron density of the fluorine atom. Nonetheless, reliable 19 F chemical-shift predictions to deduce ligand-binding modes hold great potential for in silico drug design. Herein, we present a systematic QM/MM study to predict the 19 F NMR chemical shifts of a covalently bound fluorinated inhibitor to the essential oxidoreductase tryparedoxin (Tpx) from African trypanosomes, the causative agent of African sleeping sickness. We include many protein-inhibitor conformations as well as monomeric and dimeric inhibitor-protein complexes, thus rendering it the largest computational study on chemical shifts of 19 F nuclei in a biological context to date. Our predicted shifts agree well with those obtained experimentally and pave the way for future work in this area.

Efficient calculation of NMR isotopic shifts: Difference-dedicated vibrational perturbation theory

We present difference-dedicated second-order vibrational perturbation theory (VPT2) as an efficient method for the computation of nuclear magnetic resonance (NMR) isotopic shifts, which reflect the geometry dependence of the NMR property in combination with different vibration patterns of two isotopologues. Conventional calculations of isotopic shifts, e.g., by standard VPT2, require scanning the geometry dependence over the whole molecule, which becomes expensive rapidly as the molecule size increases. In DD-VPT2, this scan can be restricted to a small region around the substitution site. At the heart of DD-VPT2 is a set of localized vibration modes common to the two isotopologues and designed such that the difference between the vibration patterns is caught by a small subset of them (usually fewer than 10). We tested the DD-VPT2 method for a series of molecules with increasing size and found that this method provides results with the same quality as VPT2 and in good agreement with the experiment, with computational savings up to 95% and less numerical instabilities. The method is easy to automatize and straightforward to generalize to other molecular properties.

Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

Sensitivity of ab Initio vs Empirical Methods in Computing Structural Effects on NMR Chemical Shifts for the Example of Peptides

The structural sensitivity of NMR chemical shifts as computed by quantum chemical methods is compared to a variety of empirical approaches for the example of a prototypical peptide, the 38-residue kaliotoxin KTX comprising 573 atoms. Despite the simplicity of empirical chemical shift prediction programs, the agreement with experimental results is rather good, underlining their usefulness. However, we show in our present work that they are highly insensitive to structural changes, which renders their use for validating predicted structures questionable. In contrast, quantum chemical methods show the expected high sensitivity to structural and electronic changes. This appears to be independent of the quantum chemical approach or the inclusion of solvent effects. For the latter, explicit solvent simulations with increasing number of snapshots were performed for two conformers of an eight amino acid sequence. In conclusion, the empirical approaches neither provide the expected magnitude nor the patterns of NMR chemical shifts determined by the clearly more costly ab initio methods upon structural changes. This restricts the use of empirical prediction programs in studies where peptide and protein structures are utilized for the NMR chemical shift evaluation such as in NMR refinement processes, structural model verifications, or calculations of NMR nuclear spin relaxation rates.

Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals

First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.

Fragment-based (13)C nuclear magnetic resonance chemical shift predictions in molecular crystals: An alternative to planewave methods

We assess the quality of fragment-based ab initio isotropic (13)C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic (13)C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.

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.

Quantum calculation of protein NMR chemical shifts based on the automated fragmentation method

The performance of quantum mechanical methods on the calculation of protein NMR chemical shifts is reviewed based on the recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. By using the Poisson-Boltzmann (PB) model and first solvation water molecules, the influence of solvent effect is also discussed. Benefiting from the fragmentation algorithm, the AF-QM/MM approach is computationally efficient, linear-scaling with a low pre-factor, and thus can be applied to routinely calculate the ab initio NMR chemical shifts for proteins of any size. The results calculated using Density Functional Theory (DFT) show that when the solvent effect is included, this method can accurately reproduce the experimental ¹H NMR chemical shifts, while the ¹³C NMR chemical shifts are less affected by the solvent. However, although the inclusion of solvent effect shows significant improvement for ¹⁵N chemical shifts, the calculated values still have large deviations from the experimental observations. Our study further demonstrates that AF-QM/MM calculated results accurately reflect the dependence of ¹³C(α) NMR chemical shifts on the secondary structure of proteins, and the calculated ¹H chemical shift can be utilized to discriminate the native structure of proteins from decoys.

Spin component-scaled second-order Møller-Plesset perturbation theory for calculating NMR shieldings

Spin component-scaled and scaled opposite-spin second-order Møller-Plesset perturbation approaches (SCS-MP2 and SOS-MP2) are introduced for calculating NMR chemical shifts in analogy to the well-established scaled approaches for MP2 energies. Gauge-including atomic orbitals (GIAO) are employed throughout this work. The GIAO-SCS-MP2 and GIAO-SOS-MP2 methods typically show superior performance to nonscaled MP2 and are closer to the coupled-cluster singles doubles perturbative triples (CCSD(T))/cc-pVQZ reference values. In addition, the pragmatic use of mixed basis sets for the Hartree-Fock and the correlated part of NMR chemical shift calculations is shown to be beneficial.

Calculating nuclear magnetic resonance shieldings using systematic molecular fragmentation by annihilation

Systematic fragmentation accurately predicts theoretical chemical shieldings.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

A linear- and sublinear-scaling method for calculating NMR shieldings in atomic orbital-based second-order Møller-Plesset perturbation theory

An atomic-orbital (AO) based formulation for calculating nuclear magnetic resonance chemical shieldings at the second-order Møller-Plesset perturbation theory level is introduced, which provides a basis for reducing the scaling of the computational effort with the molecular size from the fifth power to linear and for a specific nucleus to sublinear. The latter sublinear scaling in the rate-determining steps becomes possible by avoiding global perturbations with respect to the magnetic field and by solving for quantities that involve the local nuclear magnetic spin perturbation instead. For avoiding the calculation of the second-order perturbed density matrix, we extend our AO-based reformulation of the Z-vector method within a density matrix-based scheme. Our pilot implementation illustrates the fast convergence with respect to the required number of Laplace points and the asymptotic scaling behavior in the rate-determining steps.

An extrapolation method for the efficient calculation of molecular response properties within Born-Oppenheimer molecular dynamics

The calculation of molecular response properties in dynamic molecular systems is a major challenge that requires sampling over many steps of, e.g., Born-Oppenheimer molecular dynamics (BO-MD) simulations. We present an extrapolation scheme to accelerate such calculations for multiple steps within BO-MD trajectories or equivalently within other sampling methods of conformational space. The extrapolation scheme is related to the one introduced by Pulay and Fogarasi [Chem. Phys. Lett., 2004, 386, 272] for self-consistent field (SCF) energy calculations. We extend the extrapolation to the quantities within our density matrix-based Laplace-transformed coupled perturbed SCF (DL-CPSCF) method that allows for linear-scaling calculations of response properties for large molecular systems. Here, we focus on the example of calculating NMR chemical shifts for which the number of required DL-CPSCF iterations reduces by roughly 40-70%.

Automated Fragmentation QM/MM Calculation of Amide Proton Chemical Shifts in Proteins with Explicit Solvent Model

We have performed a density functional theory (DFT) calculation of the amide proton NMR chemical shift in proteins using a recently developed automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. Systematic investigation was carried out to examine the influence of explicit solvent molecules, cooperative hydrogen bonding effects, density functionals, size of the basis sets, and the local geometry of proteins on calculated chemical shifts. Our result demonstrates that the predicted amide proton ((1)HN) NMR chemical shift in explicit solvent shows remarkable improvement over that calculated with the implicit solvation model. The cooperative hydrogen bonding effect is also shown to improve the accuracy of (1)HN chemical shifts. Furthermore, we found that the OPBE exchange-correlation functional is the best density functional for the prediction of protein (1)HN chemical shifts among a selective set of DFT methods (namely, B3LYP, B3PW91, M062X, M06L, mPW1PW91, OB98, OPBE), and the locally dense basis set of 6-311++G**/4-31G* is shown to be sufficient for (1)HN chemical shift calculation. By taking ensemble averaging into account, (1)HN chemical shifts calculated by the AF-QM/MM approach can be used to validate the performance of various force fields. Our study underscores that the electronic polarization of protein is of critical importance to stabilizing hydrogen bonding, and the AF-QM/MM method is able to describe the local chemical environment in proteins more accurately than most widely used empirical models.

NMR shielding tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge including atomic orbitals

An efficient method for the calculation of nuclear magnetic resonance (NMR) shielding tensors is presented, which treats electron correlation at the level of second-order Mo̸ller-Plesset perturbation theory. It uses spatially localized functions to span occupied and virtual molecular orbital spaces, respectively, which are expanded in a basis of gauge including atomic orbitals (GIAOs or London atomic orbitals). Doubly excited determinants are restricted to local subsets of the virtual space and pair energies with an interorbital distance beyond a certain threshold are omitted. Furthermore, density fitting is employed to factorize the electron repulsion integrals. Ordinary Gaussians are employed as fitting functions. It is shown that the errors in the resulting NMR shielding constant, introduced (i) by the local approximation and (ii) by density fitting, are very small or even negligible. The capabilities of the new program are demonstrated by calculations on some extended molecular systems, such as the cyclobutane pyrimidine dimer photolesion with adjacent nucleobases in the native intrahelical DNA double strand (ATTA sequence). Systems of that size were not accessible to correlated ab initio calculations of NMR spectra before. The presented method thus opens the door to new and interesting applications in this area.

Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 3. Conformational Sampling and Explicit Solvents Model

Fragment-based quantum chemical calculations are able to accurately calculate NMR chemical shifts even for very large molecules like proteins. But even with systematic optimization of the level of theory and basis sets as well as the use of implicit solvents models, some nuclei like polar protons and nitrogens suffer from poor predictions. Two properties of the real system, strongly influencing the experimental chemical shifts but almost always neglected in the calculations, will be discussed here in great detail: (1) conformational averaging and (2) interactions with first-shell solvent molecules. Classical molecular dynamics simulations in explicit water were carried out for obtaining a representative ensemble including the arrangement of neighboring solvent molecules, which was then subjected to quantum chemical calculations. We could demonstrate with the small test system N-methyl acetamide (NMA) that the calculated chemical shifts show immense variations of up to 6 ppm and 50 ppm for protons and nitrogens, respectively, depending on the snapshot taken from a classical molecular dynamics simulation. Applying the same approach to the HA2 domain of the influenza virus glycoprotein hemagglutinin, a 32-amino-acid-long polypeptide, and comparing averaged values to the experiment, chemical shifts of nonpolar protons and carbon atoms in proteins were calculated with unprecedented accuracy. Additionally, the mean absolute error could be reduced by a factor of 2.43 for polar protons, and reasonable correlations were obtained for nitrogen and carbonyl carbon in contrast to all other studies published so far.