Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Dehydrogenation of ammonia on free-standing and epitaxial hexagonal boron nitride

We report a thermodynamically feasible mechanism for producing H₂ from NH₃ using hBN as a catalyst. 2D catalysts have exceptional surface areas with unique thermal and electronic properties suited for catalysis. Metal-free, 2D catalysts, are highly desirable materials that can be more sustainable than the ubiquitously employed precious and transition metal-based catalysts. Here, using density functional theory (DFT) calculations, we demonstrate that metal-free hexagonal boron nitride (hBN) is a valid alternative to precious metal catalysts for producing H₂via reaction of ammonia with a boron and nitrogen divacancy (V_BN). Our results show that the decomposition of ammonia proceeds on monolayer hBN with an activation energy barrier of 0.52 eV. Furthermore, the reaction of ammonia with epitaxially grown hBN on a Ru(0001) substrate was investigated, and we observed similar NH₃ decomposition energy barriers (0.61 eV), but a much more facile H₂ associative desorption barrier (0.69 eV vs 5.89 eV). H₂ generation from the free-standing monolayer would instead occur through a diffusion process with an energy barrier of 3.36 eV. A detailed analysis of the electron density and charge distribution along the reaction pathways was carried out to rationalise the substrate effects on the catalytic reaction.

Paramagnetic solid-state NMR assignment and novel chemical conversion of the aldehyde group to dihydrogen ortho ester and hemiacetal moieties in copper(ii)- and cobalt(ii)-pyridinecarboxaldehyde complexes

The complex chemical functionalization of aldehyde moieties in Cu(ii)- and Co(ii)-pyridinecarboxaldehyde complexes was studied. X-ray studies demonstrated that the aldehyde group (RCHO) of the four pyridine molecules is converted to dihydrogen ortho ester (RC(OCH₃)(OH)₂) and hemiacetal (RCH(OH)(OCH₃)) moieties in both 4-pyridinecarboxaldehyde copper and cobalt complexes. In contrast, the aldehyde group is retained when the 3-pyridinecarboxaldehyde ligand is complexed with cobalt. In the different copper complexes, similar paramagnetic ¹H resonance lines were obtained in the solid state; however, the connectivity with the carbon structure and the ¹H vicinities were done with 2D ¹H–¹³C HETCOR, ¹H–¹H SQ/DQ and proton spin diffusion (PSD) experiments. The strong paramagnetic effect exerted by the cobalt center prevented the observation of ¹³C NMR signals and chemical information could only be obtained from X-ray experiments. 2D PSD experiments in the solid state were useful for the proton assignments in both Cu(ii) complexes. The combination of X-ray crystallography experiments with DFT calculations together with the experimental results obtained from EPR and solid-state NMR allowed the assignment of NMR signals in pyridinecarboxaldehyde ligands coordinated with copper ions. In cases where the crystallographic information was not available, as in the case of the 3-pyridinecarboxaldehyde Cu(ii) complex, the combination of these techniques allowed not only the assignment of NMR signals but also the study of the functionalization of the substituent group.

The complex chemical functionalization of the aldehyde group was elucidated in copper and cobalt complexes for 4- and 3-pyridinecarboxaldehyde ligands.

Estimating the accuracy of calculated electron paramagnetic resonance hyperfine couplings for a lytic polysaccharide monooxygenase

Lytic polysaccharide monooxygenases (LPMOs) are enzymes that bind polysaccharides followed by an (oxidative) disruption of the polysaccharide surface, thereby boosting depolymerization. The binding process between the LPMO catalytic domain and polysaccharide is key to the mechanism and establishing structure-function relationships for this binding is therefore crucial. The hyperfine coupling constants (HFCs) from EPR spectroscopy have proven useful for this purpose. Unfortunately, EPR does not provide direct structural data and therefore the experimental EPR parameters have to be supported with parameters calculated with density functional theory. Yet, calculated HFCs are extremely sensitive to the employed computational setup. Using the LPMO Ls(AA9)A catalytic domain, we here quantify the importance of several choices in the computational setup, ranging from the use of specialized basis, the underlying structures, and the employed exchange-correlation functional. We show that specialized basis sets are an absolute necessity, and also that care has to be taken in the optimization of the underlying structure: only by allowing large parts of the protein around the active site to structurally relax could we obtain results that uniformly reproduced experimental trends. We compare our results to previously published X-ray structures and experimental HFCs for Ls(AA9)A as well as to recent experimental/theoretical results for another (AA10) family of LPMOs.

Noncollinear Relativistic Two-Component X2C Calculations of Hyperfine Couplings Using Local Hybrid Functionals. Importance of the High-Density Coordinate Scaling Limit

Local hybrid functionals with position-dependent exact-exchange admixture have been implemented in the noncollinear spin form into a two-component X2C code and are evaluated for the hyperfine coupling tensors of a series of 3d, 4d, and 5d transition-metal complexes. One aim is to see if the potential of local hybrid functionals toward an improved balance between core-shell and valence-shell spin polarization, recently identified in nonrelativistic computations on 3d complexes (Schattenberg, C.; Maier, T. M.; Kaupp, M. J. Chem. Theory Comput. 2018, 14, 5653-5672), can be extended to the hyperfine couplings of heavier metal centers. The correctness of the two-component implementation is first established by comparison to previous computations for 3d systems with or without notable spin-orbit contributions to their hyperfine tensors, and the good performance of a standard "t-LMF" local mixing function is confirmed. However, when moving to 4d and 5d metal centers, the performance of such local mixing functions deteriorates. This is likely due to their violation of the homogeneous coordinate scaling condition in the high-density limit, which is particularly important for the core shells of heavier atoms. A local mixing function that respects this high-density limit performs notably better for heavier metal centers. However, it brings in much too high exact-exchange admixtures for the 3d systems and is too inflexible to simultaneously provide reasonable chemical accuracy in other areas. These results point to the ongoing need to develop improved local mixing functions and local hybrid functionals that exhibit favorable properties in different areas of space defined by very high and much lower electron densities.

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.

Nonoxido V(IV) Complexes: Prediction of the EPR Spectrum and Electronic Structure of Simple Coordination Compounds and Amavadin

Density functional theory (DFT) calculations of the (51)V hyperfine coupling (HFC) tensor A have been completed for 20 "bare" V(IV) complexes with different donor sets, electric charges, and coordination geometries. Calculations were performed with ORCA and Gaussian software, using functionals BP86, TPSS0, B1LYP, PBE0, B3LYP, B3P, B3PW, O3LYP, BHandHLYP, BHandH, and B2PLYP. Among the basis sets, 6-311g(d,p), 6-311++g(d,p), VTZ, cc-pVTZ, def2-TZVPP, and the "core properties" CP(PPP) were tested. The experimental Aiso and Ai (where i = x or z, depending on the geometry and electronic structure of V(IV) complex) were compared with the values calculated by DFT methods. The results indicated that, based on the mean absolute percentage deviation (MAPD), the best functional to predict Aiso or Ai is the double hybrid B2PLYP. With this functional and the basis set VTZ, it is possible to predict the Aiso and Az of the EPR spectrum of amavadin with deviations of -1.1% and -2.0% from the experimental values. The results allowed us to divide the spectra of nonoxido V(IV) compounds in three types-called "type 1", "type 2", and "type 3", characterized by different composition of the singly occupied molecular orbital (SOMO) and relationship between the values of Ax, Ay, and Az. For "type 1" spectra, Az ≫ Ax ≈ Ay and Az is in the range of (135-155) × 10(-4) cm(-1); for "type 2" spectra, Ax ≈ Ay ≫ Az and Ax ≈ Ay are in the range of (90-120) × 10(-4) cm(-1); and for the intermediate spectra of "type 3", Az > Ay > Ax or Ax > Ay > Az, with Az or Ax values in the range of (120-135) × 10(-4) cm(-1). The electronic structure of the V(IV) species was also discussed, and the results showed that the values of Ax or Az are correlated with the percent contribution of V-dxy orbital in the SOMO. Similarly to V(IV)O species, for amavadin the SOMO is based mainly on the V-dxy orbital, and this accounts for the large experimental value of Az (153 × 10(-4) cm(-1)).

Coupled-Perturbed Scheme for the Calculation of Electronic g-Tensors with Local Hybrid Functionals

A coupled-perturbed Kohn-Sham (CPKS) scheme for calculating second-order magnetic properties has been developed for the case of general occupied-orbital-dependent (OOD) exchange-correlation functionals involving the exact-exchange energy density. The origin of the coupling terms in the functional derivatives of OOD functionals with respect to the orbitals has been thoroughly analyzed, and general expressions for the resulting coupling terms have been obtained. The generalized CPKS scheme thus obtained has been implemented within the MAG-ReSpect code and tested in calculations of electronic g-tensors with local hybrid functionals. Compared to previously tested global hybrids, like B3LYP, thermochemically optimized local hybrids provide only little to moderate improvement for test sets of main-group radicals and paramagnetic transition-metal complexes. Closer analyses point to possible areas in which the fundamentally more flexible local hybrids may be improved for the property at hand.

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.

First principles calculation of inhomogeneous broadening in solid-state cw-EPR spectroscopy

We present a scheme for the first-principles calculation of EPR lineshapes for continuous-wave-EPR spectroscopy (cw-EPR) of spin centers in complex chemical environments. We specifically focus on poorly characterized systems, e.g. powders and frozen glasses with variable microsolvation structures. Our approach is based on ab initio molecular dynamics simulations and ab initio calculations of the ensemble of g- and A-tensors along the trajectory. The method incorporates temperature effects as well as the full anharmonicity of the intra- and intermolecular degrees of freedom of the system. We apply this scheme to compute the lineshape of a prototypical spin probe, the nitrosodisulfonate dianionic radical (Fremy's salt), dissolved in a 50 : 50 mixture of water and methanol. We are able to determine the specific effect of variations of local solvent composition and microsolvation structure on the cw-EPR lineshape. Our molecular dynamics reveal a highly anisotropic solvation structure with distinct spatial preferences for water and methanol around Fremy's salt that can be traced back to a combination of steric and polar influences. The overall solvation structure and conformational preferences of Fremy's salt as found in our MD simulations agree very well with the results obtained from EPR and orientation-selective ENDOR spectroscopy performed on the frozen glass. The simulated EPR lineshapes show good agreement with the experimental spectra. When combined with our MD results, they characterize the lineshape dependence on local morphological fluctuations.

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.

Improving the calculation of Electron Paramagnetic Resonance hyperfine coupling tensors for d-block metals

Calculation of hyperfine coupling constants (HFCs) of Electron Paramagnetic Resonance from first principles can be a beneficial complement to experimental data in cases where the molecular structure is unknown. We have recently investigated basis set convergence of HFCs in d-block complexes and obtained a set of basis functions for the elements Sc-Zn, which were saturated with respect to both the Fermi contact and spin-dipolar components of the hyperfine coupling tensor [Hedegård et al., J. Chem. Theory Comput., 2011, 7, 4077-4087]. Furthermore, a contraction scheme was proposed leading to very accurate, yet efficient basis sets for the elements Sc-Zn. Here this scheme is tested against a larger test set of molecules and a wider range of DFT functionals. We further investigate the regular aug-cc-pVTZ and core-valence correlation aug-cc-pCVTZ basis sets as well as another core-property basis set, CP(PPP). While aug-cc-pVTZ-J provides hyperfine coupling constants that are almost identical to the converged series (aug-cc-pVTZ-Juc), we observe that not only the regular but also the core-valence correlation basis sets provide results far from the converged results. The usage of specialized core-basis sets leads to a large and highly significant improvement of the calculated hyperfine couplings in comparison with experimental data.

Optimized Basis Sets for Calculation of Electron Paramagnetic Resonance Hyperfine Coupling Constants: aug-cc-pVTZ-J for the 3d Atoms Sc-Zn

The hyperfine coupling tensor of electron paramagnetic resonance (EPR), describing the interaction between an electron and a given nuclei, depends strongly on the electron density at the nucleus. With standard Gaussian-type orbital basis sets (GTOs), employed in most calculations, it is difficult to obtain converged results of the hyperfine coupling tensor, and basis sets with more flexible core regions have therefore been devised. To this class of core property basis sets belong the aug-cc-pVTZ-J basis sets developed for the s- and p-block atoms. Here, we extend the aug-cc-pVTZ-J basis sets to include the 3d elements Sc-Zn. The converged optimal basis sets are throughout the series described by a (25s17p10d3f2g)/[17s10p7d3f2g] contraction scheme, where four tight s-, one tight p-, and one tight d-type function have been added to the original aug-cc-pVTZ basis sets. The basis sets are generally contracted, and molecular orbital coefficients are used as contraction coefficients. By validation studies with different functionals and compounds, it is shown that the values of the contraction coefficient are effectively independent of the compound used in their generation and the exchange-correlation functional employed in the calculation.

Is the spin-orbit coupling important in the prediction of the 51V hyperfine coupling constants of V(IV) O2+ species? ORCA versus Gaussian performance and biological applications

Density functional theory calculations of the (51)V hyperfine coupling (HFC) tensor A, have been completed for eighteen V(IV)O(2+) complexes with different donor set, electric charge and coordination geometry. A tensor was calculated with ORCA software with several functionals and basis sets taking into account the spin-orbit coupling contribution. The results were compared with those obtained with Gaussian 03 software using the half-and-half functional BHandHLYP and 6-311g(d,p) basis set. The order of accuracy of the functionals in the prediction of A(iso), A(z) and dipolar term A(z,anis) is BHandHLYP > PBE0 >> B3PW > TPSSh >> B3LYP >> BP86 > VWN5 (for A(iso)), BHandHLYP > PBE0 >> B3PW > TPSSh > B3LYP >> BP86 > VWN5 (for A(z)), B3LYP > PBE0 ∼ B3PW ∼ BHandHLYP >> TPSSh > BP86 ∼ VWN5 (for A(z,anis)). The good agreement in the prediction of A(z) with BHandHLYP is due to a compensation between the overestimation of A(iso) and underestimation of A(z,anis) (A(z) = A(iso) + A(z,anis)), whereas among the hybrid functionals PBE0 performs better than the other ones. BHandHLYP functional and Gaussian software are recommended when the V(IV)O(2+) species contains only V-O and/or V-N bonds, whereas PBE0 functional and ORCA software for V(IV)O(2+) complexes with one or more V-S bonds. Finally, the application of these methods to the coordination environment of V(IV)O(2+) ion in V-proteins, like vanadyl-substituted insulin, carbonic anhydrase, collagen and S-adenosylmethionine synthetase, was discussed.

Environmental effects in computational spectroscopy: accuracy and interpretation

Spectroscopic techniques are valuable tools for understanding the structure and dynamics of complex systems, such as biomolecules or nanomaterials. Most of the current research is devoted to the development of new experimental techniques for improving the intrinsic resolution of different spectra. However, the subtle interplay of several different effects acting at different length and time scales still makes the interpretation and analysis of such spectra a very difficult task. In this respect, computational spectroscopy is becoming a needful and versatile tool for the assignment and interpretation of experimental spectra. It is in fact possible nowadays to model with relatively high accuracy the physical-chemical properties of complex molecules in different environments, and to link spectroscopic evidence directly to the structural and dynamical properties of optically or magnetically active solvated probes. In this Review, significant steps toward the simulation of entire spectra in condensed phases are presented together with some basic aspects of computational spectroscopy, which highlight how intramolecular and intermolecular degrees of freedom influence several spectroscopic parameters.

Density functional restricted-unrestricted approach for nonlinear properties: application to electron paramagnetic resonance parameters of square planar copper complexes

The density functional restricted-unrestricted approach for treatments of spin polarization effects in molecular properties using spin restricted Kohn-Sham theory has been extended from linear to nonlinear properties. It is shown that the spin polarization contribution to a nonlinear property has the form of a quadratic response function that includes the zero-order Kohn-Sham operator, in analogy to the lower order case where the spin polarization correction to an expectation value has the form of a linear response function. The developed approach is used to formulate new schemes for computation of electronic g-tensors and hyperfine coupling constants, which include spin polarization effects within the framework of spin restricted Kohn-Sham theory. The proposed computational schemes are in the present work employed to study the spin polarization effects on electron paramagnetic resonance spin Hamiltonian parameters of square planar copper complexes. The obtained results indicate that spin polarization gives rise to sizable contributions to the hyperfine coupling tensor of copper in all investigated complexes, while the electronic g-tensors of these complexes are only marginally affected by spin polarization and other factors, such as choice of exchange-correlation functional or molecular structures, will have more pronounced impact on the accuracy of the results.

Computational studies of EPR parameters for paramagnetic molybdenum complexes. II. Larger MoV systems relevant to molybdenum enzymes

The careful validation of modern density functional methods for the computation of electron paramagnetic resonance (EPR) parameters in molybdenum complexes has been extended to a number of low-symmetry MoV systems that model molybdoenzyme active sites. Both g and hyperfine tensors tend to be reproduced best by hybrid density functionals with about 30-40% exact-exchange admixture, with no particular spin contamination problems encountered. Spin-orbit corrections to hyperfine tensors are mandatory for quantitative and, in some cases, even for qualitative agreement. The g11 (g||) component of the g tensor tends to come out too positive when spin-orbit coupling is included only to leading order in perturbation theory. Compared to single-crystal experiments, the calculations reproduce both g- and hyperfine-tensor orientations well, both relative to each other and to the molecular framework. This is significant, as simulations of the EPR spectra of natural-abundance frozen-solution samples frequently do not allow a reliable determination of the hyperfine tensors. These may now be extracted based on the quantum-chemically calculated parameters. In a number of cases, revised simulations of the experimental spectra have brought theory and experiment into substantially improved agreement. Systems with two terminal oxo ligands, and to some extent with an oxo and a sulfido ligand, have been confirmed to exhibit particularly large negative Deltag33 shifts and thus large g anisotropies. This is discussed in the context of the experimental data for xanthine oxidase.

QM/MM calculations with DFT for taking into account protein effects on the EPR and optical spectra of metalloproteins. Plastocyanin as a case study

A detailed study of the influence of the surrounding protein on magnetic and optical spectra of metalloproteins is presented using the quantum-mechanical/molecular mechanical (QM/MM) approach. The well-studied type I copper site in plastocyanin in the cupric oxidation state is taken as a test case because its spectroscopic properties have been extensively studied and are well understood. The calculations have been performed using nonrelativistic and scalar relativistic (at the level of the zeroth order regular approximation, ZORA) calculations (B3LYP functional). Linear response theory has been used to calculate first- and second-order properties, namely the EPR g-tensor, the central metal hyperfine couplings (HFCs), the HFCs of the directly coordinating ligands, as well as superhyperfine couplings (1H, 14N) from remote nuclei, transition energies, and oscillator strengths. Two different model systems have been defined that do not and do include important amino acids from the second coordination sphere, respectively. For comparison, calculations have been carried out in the gas phase and in a dielectric continuum (conductor like screening model, COSMO) with a dielectric constant of four. The best results were obtained at the scalar relativistic ZORA level for the largest model in conjunction with explicit modeling of the protein environment through the QM/MM procedure, which is also considered to be the highest level of theory used in this work. The protein effects beyond the second coordination sphere were found to be quite substantial (up to 30% changes on some properties), and were found to require an explicit treatment of the protein beyond the second coordination sphere. In addition, the embedding water cage was found to have a nonnegligible influence on the calculated spectroscopic data, which is of the same order as the influence of the protein backbone charges. However, while qualitatively satisfactory, the errors in the calculated spectroscopic parameters are still substantial, and can all be traced back to the fact that the linear-response of the presently available functionals is "too stiff" with respect to the external perturbations at least for the model systems studied here. Ligand field-based approaches are used to correct for systematic errors in the DFT procedures. As a consequence, we propose a new breakdown of the copper hyperfine interaction into Fermi-contact, spin-dipolar and spin-orbit contributions.

Halogen bonds between 2,2,6,6-tetramethylpiperidine-N-oxyl radical and CxHyFzI species: DFT calculations of physicochemical properties and comparison with hydrogen bonded adducts

Structural, thermodynamic, and magnetic properties of adducts between the 2,2,6,6-tetramethylpiperidine-N-oxyl radical and representative hydrogen and halogen bond donors in solution have been investigated by an integrated computational tool including hybrid density functionals and discrete-continuum solvent models. From a quantitative point of view, the computed values show a fair agreement with experiment when environmental effects are taken into the proper account. From a more general point of view, our analysis points out a number of analogies, but also some difference, between hydrogen and halogen bond, which have been interpreted in terms of the various effects tuning thermodynamic and spectroscopic parameters.

Interplay of Intrinsic, Environmental, and Dynamic Effects in Tuning the EPR Parameters of Nitroxides: Further Insights from an Integrated Computational Approach

The role of stereoelectronic, environmental, and short-time dynamic effects in tuning the hyperfine and gyromagnetic tensors of a prototypical nitroxide spin probe has been investigated by an integrated computational approach based on extended Lagrangian molecular dynamics and discrete-continuum solvent models. Trajectories were generated in two protic solvents as well as in the gas phase for reference; structural analysis of the dynamics, and comparison with optimized solute-solvent clusters, allowed for the identification of the prevailing solute-solvent hydrogen-bonding patterns and helped to define the strategy for the computation of magnetic parameters. This was performed in a separate step, on a large number of frames, by a high-level DFT approach coupling the PBE0 hybrid functional with a tailored basis set and with proper account of specific and bulk solvent effects. Remarkable changes in solvation networks are found on going from aqueous to methanol solution, thus providing a rationalization of indirect experimentally available evidence. The computed magnetic parameters are in satisfactory agreement with the available measured values and allow for an unbiased evaluation of the role of different effects in tuning the overall EPR observables. Apart from their intrinsic interest, our results pave the route toward the development of tunable detection protocols based on specific spectroscopic signatures.

Computational Studies of Electron Paramagnetic Resonance Parameters for Paramagnetic Molybdenum Complexes. 1. Method Validation on Small and Medium-Sized Systems

A variety of density functional methods have been evaluated in the computation of electronic g-tensors and molybdenum hyperfine couplings for systems ranging from the Mo atom through MoIIIN, [MoVOCl4]-, and [MoVOF5]2- to two larger MoV complexes MoXLCl2 (X=O, S; L=tris(3,5-dimethylpyrazolyl)hydroborate anion). In particular, the influence of the molybdenum basis set and of various exchange-correlation functionals with variable admixtures of Hartree-Fock exchange on the computed EPR parameters have been evaluated in detail. Careful basis-set studies have provided a moderate-sized 12s6p5d all-electron basis on molybdenum that gives hyperfine tensors in excellent agreement with much larger basis sets and that will be useful for calculations on larger systems. The best agreement with experimental data for both hyperfine and g-tensors is obtained with hybrid functionals containing approximately 30-40% Hartree-Fock exchange. Only for MoSLCl2 does increasing spin contamination with increasing exact-exchange admixture restrict the achievable computational accuracy. In all cases, spin-orbit corrections to the hyperfine tensors are sizable and have to be included in accurate calculations. Scalar relativistic effects enhance the isotropic Mo hyperfine coupling by approximately 15-20%. Two-component g-tensor calculations with variational inclusion of spin-orbit coupling show that the Deltag parallel components in [MoVOCl4]- and [MoVOF5]2- depend on higher-order spin-orbit contributions and are thus described insufficiently by the usual second-order perturbation approaches. Computed orientations of g- and hyperfine tensors relative to each other and to the molecular framework for the MoXLCl2 complexes provide good agreement between theory and single-crystal electron paramagnetic resonance experiments. In these cases, the hyperfine tensor orientations are influenced only slightly by spin-orbit effects.

The performance of semilocal and hybrid density functionals in 3d transition-metal chemistry

We investigate the performance of contemporary semilocal and hybrid density functionals for bond energetics, structures, dipole moments, and harmonic frequencies of 3d transition-metal (TM) compounds by comparison with gas-phase experiments. Special attention is given to the nonempirical metageneralized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], which has been implemented in TURBOMOLE for the present work. Trends and error patterns for classes of homologous compounds are analyzed, including dimers, monohydrides, mononitrides, monoxides, monofluorides, polyatomic oxides and halogenides, carbonyls, and complexes with organic pi ligands such as benzene and cyclopentadienyl. Weakly bound systems such as Ca(2), Mn(2), and Zn(2) are discussed. We propose a reference set of reaction energies for benchmark purposes. Our all-electron results with quadruple zeta valence basis sets validate semilocal density-functional theory as the workhorse of computational TM chemistry. Typical errors in bond energies are substantially larger than in (organic) main group chemistry, however. The Becke-Perdew'86 [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 33, 8822 (1986)] GGA and the TPSS meta-GGA have the best price/performance ratio, while the TPSS hybrid functional achieves a slightly lower mean absolute error in bond energies. The popular Becke three-parameter hybrid B3LYP underbinds significantly and tends to overestimate bond distances; we give a possible explanation for this. We further show that hybrid mixing does not reduce the width of the error distribution on our reference set. The error of a functional for the s-d transfer energy of a TM atom does not predict its error for TM bond energies and bond lengths. For semilocal functionals, self-interaction error in one- and three-electron bonds appears to be a major source of error in TM reaction energies. Nevertheless, TPSS predicts the correct ground-state symmetry in the vast majority of cases and rarely fails qualitatively. This further confirms TPSS as a general purpose functional that works throughout the periodic table. We also give workstation timing comparisons for the 645-atom protein crambin.

Protein–cofactor interactions in bacterial reaction centers from Rhodobacter sphaeroides R-26: Effect of hydrogen bonding on the electronic and geometric structure of the primary quinone. A density functional theory study

The effect of hydrogen bonding to the primary quinone (Q(A) and Q(*)(-)(A)) in bacterial reaction centers was studied using density functional theory (DFT) calculations. The charge neutral state Q(A) was investigated by optimizing the hydrogen atom positions of model systems extracted from 15 different X-ray structures. From this analysis, mean values of the H-bond lengths and directions were derived. It was found that the N(delta)-H of His M219 forms a shorter H-bond to Q(A) than the N-H of Ala M260. The H-bond of His M219 is linear and more twisted out of the quinone plane. The radical anion Q(*)(-)(A) in the protein environment was investigated by using a mixed quantum mechanics/molecular mechanics (QM/MM) approach. Two geometry optimizations with a different number of flexible atoms were performed. H-bond lengths were obtained and spectroscopic parameters calculated, i.e. the hyperfine and nuclear quadrupole couplings of magnetic nuclei coupled to the radical. Good agreement was found with the results provided by EPR/ENDOR spectroscopy. This implies that the calculated lengths and directions of the H-bonds to Q(*)(-)(A) are reliable values. From a comparison of the neutral and reduced state of Q(A) it was concluded that the H-bond distances are shortened by approximately 0.17 Angstroms (His M219) and approximately 0.13 Angstroms (Ala M260) upon single reduction of the quinone. It is shown that the point-dipole approximation can not be used for an estimation of H-bond lengths from measured hyperfine couplings in a system with out-of-plane H-bonding. In contrast, the evaluation of the nuclear quadrupole couplings of (2)H nuclei substituted in the hydrogen bonds yields H-bond lengths close to the values that were deduced from DFT geometry optimizations. The significance of hydrogen bonding to the quinone cofactors in biological systems is discussed.

Relativistic Density Functional Calculations of EPR g Tensor for η{CuNO}11 Species in Discrete and Zeolite-Embedded States

Spin-unrestricted zeroth order regular approximation (ZORA) and the scalar relativistic method based on Pauli Hamiltonian implemented in the Amsterdam Density Functional suite were used to calculate the electronic g tensor for isolated covalent {CuNO}(11) and electrostatic {q-NO}(1) species and for various model molecular and nonmolecular {CuNO}(11)-containing systems, epitomizing copper nitrosyl cage adducts in the ZSM-5 zeolite. The predicted g tensor values using the ZORA/VWN scheme were in satisfactory agreement with experimental EPR results. Relativistic, diamagnetic, and paramagnetic contributions to the calculated g tensor were quantified. The nature of the observed Deltag shifts was discussed in terms of the molecular orbital contributions due to the magnetic field-induced couplings and their structure sensitivity. The influence of basis set and exchange-correlation functional on the results was also briefly evaluated.

Determination of the g-Tensors and Their Orientations for cis,trans-(L-N2S2)MoVOX (X = Cl, SCH2Ph) by Single-Crystal EPR Spectroscopy and Molecular Orbital Calculations

A single-crystal study of cis,trans-(L-N2S2)MoVOCl (1) doped into cis,trans-(N2S2)MoVIO2 (3) has enabled the g-tensor of 1 and its orientation with respect to the molecular structure to be determined. The EPR parameters (g1, 2.004; g2, 1.960; g3, 1.946; A1, 71.7 x 10(-4) cm(-1); A2, 11.7 x 10(-4) cm(-1); A3, 32.0 x 10(-4) cm(-1)) of cis,trans-(L-N2S2)MoVOCl [L-N2S2H2 = N,N'-dimethyl-N,N'-bis(mercaptophenyl)ethylenediamine] mimic those of the low-pH form of sulfite oxidase and the "very rapid" species of xanthine oxidase. The principal axis that corresponds to g1 is rotated approximately 10 degrees from the Mo[triple bond]O vector, while the principal axis that corresponds to g3 is located in the equatorial plane and approximately 38 degrees from the Mo-Cl vector. Independent theoretical calculations of the g-tensor of 1 were performed using two types of techniques: (1) the spectroscopically parametrized intermediate neglect of differential overlap technique (INDO/S) combined with single-excitation configuration interaction (CIS); (2) a scalar relativistic DFT (BP86 and B3LYP functionals) treatment using the zeroth order regular approximation to relativistic effects (ZORA) in combination with recently developed accurate multicenter mean field spin-orbit operators (RI-SOMF) and the estimation of solvent effects using dielectric continuum theory at the conductor-like screening model (COSMO) level. The excellent agreement between experiment and theory, as well as the high consistency between the INDO/S and BP86/ZORA results, provides a sound basis for analysis of the calculated orientation of the g-tensor for cis,trans-(L-N2S2)MoVO(SCH2Ph) (2), for which single-crystal EPR data are not available but which contains three equatorial sulfur donor atoms, as occurs in sulfite oxidase and xanthine oxidase. The implications of these results for the EPR spectra of the Mo(V) centers of enzymes are discussed.