Basis Sets Of Quality Research Articles

Is explicitly correlated double-hybrid density functional theory advantageous for vibrational frequencies?

We have investigated the effect of F12 geminals on the basis set convergence of harmonic frequencies calculated using two representative double-hybrid density functionals, namely, B2GP-PLYP and revDSD-PBEP86-D4. Like previously found for energetics (Mehta N.; Martin J. M. L. J. Chem. Theory Comput. 2022, 18, 5978), one sees an acceleration by two zeta steps, such that even the cc-pVDZ-F12 basis set is quite close to the complete basis set (CBS) limit. However, the basis set convergence problem is not as acute as for energetics, and compared with experimental harmonic frequencies, conventional orbital calculations with augmented triple zeta quality basis set are acceptably close to the CBS limit, and can be carried out using analytical second derivatives. An efficient implementation of double-hybrid F12 analytical derivatives would make the F12 approach attractive in the sense that even an spd orbital basis set would be adequate. For the accurate revDSD-PBEP86-D4 functional, the role of differing local correlation terms (Perdew–Zunger 1981 versus VWN5) in different electronic structure programs has been investigated, while optimal double-hybrid parameters and performance statistics for energetics as well as frequencies differ slightly between the two implementations; these differences are insignificant for practical purposes.

The van der Waals interactions in systems involving superheavy elements: the case of oganesson (Z = 118).

This work presents a study involving dimers composed of He, Ne, Ar, Kr, Xe, Rn, and Og noble gases with oganesson, a super-heavy closed-shell element (Z = 118). He-Og, Ne-Og, Ar-Og, Kr-Og, Xe-Og, Rn-Og, and Og-Og ground state electronic potential energy curves were calculated based on the 4-component (4c) Dirac-Coulomb Hamiltonian and were counterpoise corrected. For the 4c calculations, the electron correlation was taken into account using the same methodology (MP2-srLDA) and basis set quality (Dyall's acv3z and Dunning's aug-cc-PVTZ). All calculations included quantum electrodynamics effects at the Gaunt interaction level. For all the aforementioned dimers the vibration energies, spectroscopic constants (ωe, ωexe, ωeye, αe, and γe), and lifetime as a function of the temperature (which ranged from 200 to 500 K) were also calculated. The obtained results suggest that the inclusion of quantum electrodynamics effects reduces the value of the dissociation energy of all hetero-nuclear molecules with a percentage contribution ranging from 0.48% (for the He-Og dimer) to 9.63% (for the Rn-Og dimer). The lifetime calculations indicate that the Og-He dimer is close to the edge of instability and that Ng-Og dimers are relatively less stable when the Gaunt correction is considered. Exploiting scaling laws that adopt the polarizability of involved partners as scaling factors, it has also been demonstrated that in such systems the interaction is of van der Waals nature (size repulsion plus dispersion attraction) and this permitted an estimation of dissociation energy and equilibrium distance in the Og-Og dimer. This further information has been exploited to evaluate the rovibrational levels in this symmetric dimer and to cast light on the macroscopic properties of condensed phases concerning the complete noble gas family, emphasizing some anomalies of Og.

From cyclic (alkyl)(amino)carbene (CAAC) precursors to fluorinating reagents. Experimental and theoretical study.

Addition of anhydrous HF to the hydrochloride [MeCAACH][Cl(HCl)0.5] resulted in the formation of salts with high HF content. By stepwise removal of HF in vacuo, we selectively prepared [MeCAACH][F(HF)2] (3) and [MeCAACH][F(HF)3] (4). We also characterised a salt with [F(HF)4]- anions within the structure of [MeCAACH][F(HF)3.5] (5). Compounds with a lower content of HF were not accessible under vacuum conditions. MeCAAC(H)F (1) was selectively prepared by abstraction of HF from 3 with CsF or KF, while [MeCAACH][F(HF)] (2) was prepared by mixing 3 and 1 in a 1 : 1 ratio. Compound 2 proved to be quite unstable as it tends to disproportionate into 1 and 3. This observation triggered our computational study, in which the structural relationships between CAAC-based fluoropyrrolidines and dihydropyrrolium fluorides were investigated using different DFT methods. The study showed that the results were very sensitive to the computational method used. For a correct description, the quality of the triple-ζ basis set was crucial. Surprisingly, the isodesmic reaction of [MeCAACH][F] + [MeCAACH][F(HF)2] → [MeCAACH][F(HF)] + [MeCAACH][F(HF)] did not confirm the low thermodynamic stability of 2. Furthermore, the use of 3 as a nucleophilic fluorinating reagent was tested on a range of organic substrates, as it is the most stable compound in this series. It was found to have the potential to fluorinate benzyl bromides, 1- and 2-alkyl bromides, silanes and sulfonyls with good to excellent yields of the target fluorides.

A deep transfer learning-based protocol accelerates full quantum mechanics calculation of protein.

Effective full quantum mechanics (FQM) calculation of protein remains a grand challenge and of great interest in computational biology with substantial applications in drug discovery, protein dynamic simulation and protein folding. However, the huge computational complexity of the existing QM methods impends their applications in large systems. Here, we design a transfer-learning-based deep learning (TDL) protocol for effective FQM calculations (TDL-FQM) on proteins. By incorporating a transfer-learning algorithm into deep neural network (DNN), the TDL-FQM protocol is capable of performing calculations at any given accuracy using models trained from small datasets with high-precision and knowledge learned from large amount of low-level calculations. The high-level double-hybrid DFT functional and high-level quality of basis set is used in this work as a case study to evaluate the performance of TDL-FQM, where the selected 15 proteins are predicted to have a mean absolute error of 0.01kcal/mol/atom for potential energy and an average root mean square error of 1.47kcal/mol/$ {\rm A^{^{ \!\!\!o}}} $ for atomic forces. The proposed TDL-FQM approach accelerates the FQM calculation more than thirty thousand times faster in average and presents more significant benefits in efficiency as the size of protein increases. The ability to learn knowledge from one task to solve related problems demonstrates that the proposed TDL-FQM overcomes the limitation of standard DNN and has a strong power to predict proteins with high precision, which solves the challenge of high precision prediction in large chemical and biological systems.

Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H3PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

The four-component DFT method for the calculation of the EPR g-tensor using a restricted magnetically balanced basis and London atomic orbitals.

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functional theory (DFT) method for calculating the g-tensor, incorporating both the GIAOs and RMB basis and based on the Dirac-Coulomb Hamiltonian. The approach utilizes the state-of-the-art noncollinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results and inclusion of spin-polarization effects in the calculation. We also show that the gauge dependence of the results obtained is connected to the nonvanishing integral of the current density in a finite basis, explain why the results of cluster calculations exhibit surprisingly low gauge dependence, and demonstrate that the gauge problem disappears for systems with certain point-group symmetries.

New pecJ-n (n = 1, 2) Basis Sets for High-Quality Calculations of Indirect Nuclear Spin-Spin Coupling Constants Involving 31P and 29Si: The Advanced PEC Method.

In this paper, we presented new J-oriented basis sets, pecJ-n (n = 1, 2), for phosphorus and silicon, purposed for the high-quality correlated calculations of the NMR spin–spin coupling constants involving these nuclei. The pecJ-n basis sets were generated using the modified version of the property-energy consistent (PEC) method, which was introduced in our earlier paper. The modifications applied to the original PEC procedure increased the overall accuracy and robustness of the generated basis sets in relation to the diversity of electronic systems. Our new basis sets were successfully tested on a great number of spin–spin coupling constants, involving phosphorus or/and silicon, calculated within the SOPPA(CCSD) method. In general, it was found that our new pecJ-1 and pecJ-2 basis sets are very efficient, providing the overall accuracy that can be characterized by MAEs of about 3.80 and 1.98 Hz, respectively, against the benchmark data obtained with a large dyall.aae4z+ basis set of quadruple-ζ quality.

Mechanisms of Complete Dissociation of CO2 on Iron Clusters.

Dissociation of CO2 on iron clusters was studied by using semilocal density functional theory and basis sets of triple-zeta quality. Fe2 , Fe4 , and Fe16 clusters were selected as the representative host clusters. When searching for isomers of Fen CO2 , n=2, 4 and 16 corresponding to carbon dioxide attachment to the host clusters, its reduction to O and CO, and to the complete dissociation, it was found that the total spin magnetic moments of the lowest energy states of the isomers are often quenched with respect to those of initial reagents Fen +CO2 . Dissociation pathways of the Fe2 +CO2 , Fe4 +CO2 , and Fe16 +CO2 reactions contain several transition states separated by the local minima states; therefore, a natural question is where do the spin flips occur? Since lifetimes of magnetically excited states were shown to be of the order of 100 fs, the search for the CO2 dissociation pathways was performed under the assumption that magnetic deexcitation may occur at the intermediate local minima. Two dissociation pathways were obtained for each Fen +CO2 reaction using the gradient-based methods. It was found that the Fe2 +CO2 reaction is endothermic with respect to both reduction and complete dissociation of CO2 , whereas the Fe4 +CO2 and Fe16 +CO2 reactions are exothermic to both reduction and complete dissociation of carbon dioxide. The CO2 reduction was found to be more favorable than its complete dissociation in the Fe4 case.

Performance of a one-parameter correlation factor for transcorrelation: Study on a series of second row atomic and molecular systems.

In this work, we investigate the performance of a recently proposed transcorrelated (TC) approach based on a single-parameter correlation factor [E. Giner, J. Chem. Phys. 154, 084119 (2021)] for systems involving more than two electrons. The benefit of such an approach relies on its simplicity as efficient numerical-analytical schemes can be set up to compute the two- and three-body integrals occurring in the effective TC Hamiltonian. To obtain accurate ground state energies within a given basis set, the present TC scheme is coupled to the recently proposed TC-full configuration interaction quantum Monte Carlo method [Cohen et al., J. Chem. Phys. 151, 061101 (2019)]. We report ground state total energies on the Li-Ne series, together with their first cations, computed with increasingly large basis sets and compare to more elaborate correlation factors involving electron-electron-nucleus coordinates. Numerical results on the Li-Ne ionization potentials show that the use of the single-parameter correlation factor brings on average only a slightly lower accuracy (1.2 mH) in a triple-zeta quality basis set with respect to a more sophisticated correlation factor. However, already using a quadruple-zeta quality basis set yields results within chemical accuracy to complete basis set limit results when using this novel single-parameter correlation factor. Calculations on the H2O, CH2, and FH molecules show that a similar precision can be obtained within a triple-zeta quality basis set for the atomization energies of molecular systems.

DFT Calculations of 31P NMR Chemical Shifts in Palladium Complexes.

In this study, comparative analysis of calculated (GIAO method, DFT level) and experimental 31P NMR shifts for a wide range of model palladium complexes showed that, on the whole, the theory reproduces the experimental data well. The exceptions are the complexes with the P=O phosphorus, for which there is a systematic underestimation of shielding, the value of which depends on the flexibility of the basis sets, especially at the geometry optimization stage. The use of triple-ζ quality basis sets and additional polarization functions at this stage reduces the underestimation of shielding for such phosphorus atoms. To summarize, in practice, for the rapid assessment of 31P NMR shifts, with the exception of the P=O type, a simple PBE0/{6-311G(2d,2p); Pd(SDD)}//PBE0/{6-31+G(d); Pd(SDD)} approximation is quite acceptable (RMSE = 8.9 ppm). Optimal, from the point of view of “price–quality” ratio, is the PBE0/{6-311G(2d,2p); Pd(SDD)}//PBE0/{6-311+G(2d); Pd(SDD)} (RMSE = 8.0 ppm) and the PBE0/{def2-TZVP; Pd(SDD)}//PBE0/{6-311+G(2d); Pd(SDD)} (RMSE = 6.9 ppm) approaches. In all cases, a linear scaling procedure is necessary to minimize systematic errors.

Fragmentation Method for Computing Quantum Mechanics and Molecular Mechanics Gradients for Force Matching: Validation with Hydration Free Energy Predictions Using Adaptive Force Matching.

A fragmentation approach referred to as a simple overlapping region method for force matching (SORForM) is presented. SORForM is designed to enable efficient computation of quantum mechanical (QM) forces for large molecules and is validated in the framework of adaptive force matching (AFM) to develop solute models in water. The SORForM method divides a molecule into overlapping QM regions with each region containing a gradient zone and a buffer zone. The buffer zone ensures that the atoms in the gradient zone have their surroundings unchanged with fragmentation. The performance of the method is validated with mefenamic acid and linalyl acetate by comparing the hydration free energies of AFM models developed with and without SORForM. The AFM hydration free energies are also compared with that of the experiments. The models developed with B3LYP-D3(BJ) and def2-TZVP are in excellent agreement with experiments. Our work shows that PBE-D3(BJ) provides less satisfactory results when compared to B3LYP-D3(BJ). The def2-TZVP basis set is found to greatly improve the agreement with experiments when compared to a double-zeta quality basis set.

Metal-organic frameworks properties from hybrid density functional approximations.

The chemical versatility and modular nature of Metal-Organic Frameworks (MOFs) make them unique hybrid inorganic-organic materials for several important applications. From a computational point of view, ab initio modeling of MOFs is a challenging and demanding task, in particular, when the system reaches the size of gigantic MOFs as MIL-100 and MIL-101 (where MIL stands for Materials Institute Lavoisier) with several thousand atoms in the unit cell. Here, we show how such complex systems can be successfully tackled by a recently proposed class of composite electronic structure methods revised for solid-state calculations. These methods rely on HF/density functional theory hybrid functionals (i.e., PBEsol0 and HSEsol) combined with a double-zeta quality basis set. They are augmented with semi-classical corrections to take into account dispersive interactions (D3 scheme) and the basis set superposition error (gCP). The resulting methodologies, dubbed "sol-3c," are cost-effective yet reach the hybrid functional accuracy. Here, sol-3c methods are effectively applied to predict the structural, vibrational, electronic, and adsorption properties of some of the most common MOFs. Calculations are feasible even on very large MOFs containing more than 2500 atoms in the unit cell as MIL-100 and MIL-101 with reasonable computing resources. We propose to use our composite methods for the routine in silico screening of MOFs targeting properties beyond plain structural features.

Investigation of the low-lying electronic states of sulfur monofluoride cation

High-level ab initio computations are performed for the low-lying Λ-S and Ω electronic states of SF+, with the icMRCI+Q methodology coupled with basis sets of quintuple-ζ quality. The manifolds of electronic states correlating with the first and second dissociation limits are well determined. Electronic structures of all excited states investigated are characterized for the first time. Dipole moments of all states are obtained, and trends of polarity variations are discussed. Transition probabilities, such as transition dipole moments, Franck-Condon factors, vibrational branching ratios and radiative lifetimes, are also calculated for selected transition bands. We have also performed a parallel calculation for the SF radical to verify our computational accuracy. From comparative studies on associated parameters derived in this work and those reported in literature, a mutually satisfactory agreement is noticed, indicating our data and results are trustworthy.

Effect of Internal Donors on Raman and IR Spectroscopic Fingerprints of MgCl2/TiCl4 Nanoclusters Determined by Machine Learning and DFT.

To go deep into the origin of MgCl supported Ziegler-Natta catalysis we need to fully understand the structure and properties of precatalytic nanoclusters MgCl/TiCl in presence of Lewis bases as internal donors (ID). In this work MgCl/TiCl nanoplatelets derived by machine learning and DFT calculations have been used to model the interaction with ethyl-benzoate EB as ID, with available exposed sites of binary TiCl/MgCl systems. The influence of vicinal TiCl and coadsorbed TiCl on energetic, structural and spectroscopic behaviour of EB has been considered. The adsorption of homogeneous-like TiClEB and TiCl(EB) at the various surface sites have been also simulated. B3LYP-D2 and M06 functionals combined with TZVP quality basis set have been adopted for calculations. The adducts have been characterized by computing IR and Raman spectra that have been found to provide specific fingerprints useful to identify surface species; IR spectra have been successfully compared to available experimental data.

Interactions of Si+(2PJ) and Ge+ (2PJ) with rare gas atoms (He-Rn): interaction potentials, spectroscopy, and ion transport coefficients.

Accurate interatomic potentials were calculated for the interaction of a singly-charged silicon cation, Si+, with a single rare gas atom, RG (RG = Kr-Rn), as well as a singly-charged germanium cation, Ge+, with a single rare gas atom, RG (RG = He-Rn). The RCCSD(T) method and basis sets of quadruple-ζ and quintuple-ζ quality were employed; each interaction energy is counterpoise corrected and extrapolated to the basis set limit. The lowest electronic term (2P) of each cation was considered, and the interatomic potentials calculated for the diatomic terms that arise from these: 2Π and 2Σ+. Additionally, the interatomic potentials for the respective spin-orbit levels were calculated, and the effect on the spectroscopic parameters was examined. Variations in several spectroscopic parameters with the increasing atomic number of RG were examined. The presence of incipient chemical interaction was also examined via Birge-Sponer-like plots and various population analyses across the series. In the cases of heavier RG, these were consistent with a small amount of electron transfer from the heavier RG atom to the cation, rationalizing the spin-orbit splittings. This was also supported by the observed larger-than-expected spin-orbit splittings for the Si+-RG complexes. Finally, each set of RCCSD(T) potentials including spin-orbit coupling was employed to calculate transport coefficients for the cation moving through a bath of the RG. The calculated ion mobilities showed significant differences for the two atomic spin-orbit states, arising from subtle changes in the interaction potentials.

A quantum-chemically supported classical approach to assessing the vibrational contribution to the thermal expansion of molecules. Example of LaI3

А dynamic vibrational task has been solved with taking into account the interaction of vibrational coordinates on the base of the calculated PES. The vibrational level energies and corresponding wave functions of LaI3 molecule have been determined by the solution of three-dimensional Schrödinger equations. Theoretical calculations were performed by the DFT/PBE0, DFT/B3LYP and MP2 methods using relativistic effective pseudopotentials and a good quality basis sets for inner and outer atomic shells. Six-dimensional PES was numerically calculated by the DFT/PBE0 approach. Available gas-phase electron diffraction (GED) data were simulated by the original methodology based on the full dimensional PES. A good agreement between experimental and theoretical thermal average structural parameters supports the reliability of the theoretical data and the efficiency of the methodology implemented. It is shown that the standard approaches based on the use of the harmonic approximation, to calculate of the vibrational corrections necessary for the interpretation of GED results, at high temperatures lead to either significantly overestimated or underestimated values of equilibrium geometrical parameters. An analysis of the anharmonic vibrational levels obtained indicates the absence of Fermi resonances and the suitability of the harmonic approximation for describing fundamental vibrational transitions.

ZORA double zeta basis sets for fifth row elements: Application in studies of electronic structures of atoms and molecules

Segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) to be used with the zero-order regular approximation (ZORA) scalar relativistic Hamiltonian was developed for the elements Cs, Ba, La, and from Hf to Rn. This set was augmented with diffuse functions for the purpose of describing electrons distant from atomic nuclei. Using the ZORA-B3LYP method, some atomic and molecular properties are computed. Benchmark theoretical results and experimental data were used to evaluate the performance of the DZP-ZORA and ADZP-ZORA basis sets. Despite their small sizes, these sets have proven to be accurate and reliable and can also be used in property calculations involving electrons not only from the outer shells, but also from the inner shells. Comparison of second order Douglas-Kroll-Hess and ZORA results was made.

Property-optimized Gaussian basis sets for lanthanides

Property-optimized Gaussian basis sets of split-valence, triple-zeta valence, and quadruple-zeta valence quality are developed for the lanthanides Ce-Lu for use with small-core relativistic effective core potentials. They are constructed in a systematic fashion by augmenting def2 orbital basis sets with diffuse basis functions and minimizing negative static isotropic polarizabilities of lanthanide atoms with respect to basis set exponents within the unrestricted Hartree-Fock method. The basis set quality is assessed using a test set of 70 molecules containing the lanthanides in their common oxidation states and f electron occupations. 5d orbital occupation turns out to be the determining factor for the basis set convergence of polarizabilities in lanthanide atoms and the molecular test set. Therefore, two series of property-optimized basis sets are defined. The augmented def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets balance the accuracy of polarizabilities across lanthanide oxidation states. The relative errors in atomic and molecular polarizability calculations are ≤8% for augmented split-valence basis sets, ≤ 2.5% for augmented triple-zeta valence basis sets, and ≤1% for augmented quadruple-zeta valence basis sets. In addition, extended def2-TZVPPDD and def2-QZVPPDD are provided for accurate calculations of lanthanide atoms and neutral clusters. The property-optimized basis sets developed in this work are shown to accurately reproduce electronic absorption spectra of a series of LnCp3 '- complexes (Cp' = C5H4SiMe3, Ln = Ce-Nd, Sm) with time-dependent density functional theory.

The curious case of DMSO: A CCSD(T)/CBS(aQ56+d) benchmark and DFT study.

This work addresses the pathological behavior of the energetics of dimethyl sulfoxide and related sulfur-containing compounds by providing the computational benchmark energetics of R2E2 species, where R = H/CH3 and E = O/S, with bent and pyramidal geometries using state-of-the-art methodologies. These 22 geometries were fully characterized with coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)], second-order Møller-Plesset perturbation theory (MP2), and 22 density functional theory (DFT) methods with 8, 12, and 12, respectively, correlation consistent basis sets of double-, triple-, or quadruple-ζ quality. The relative energetics were determined at the MP2 and CCSD(T) complete basis set (CBS) limits using 17 basis sets up to sextuple-ζ and include augmented, tight-d, and core-valence correlation consistent basis sets. The relative energies of oxygen-/sulfur-containing compounds exhibit exceptionally slow convergence to the CBS limit with canonical methods as well as significant basis set dependence. CCSD(T) with quadruple-ζ basis sets can give qualitatively incorrect relative energies. Explicitly correlated MP2-F12 and CCSD(T)-F12 methods dramatically accelerate the convergence of the relative energies to the CBS limit for these problematic compounds. The F12 methods with a triple-ζ quality basis set give relative energies that deviate no more than 0.41kcal mol-1 from the benchmark CBS limit. The correlation consistent Composite Approach (ccCA), ccCA-TM (TM for transition metals), and G3B3 deviated by no more than 2kcal mol-1 from the benchmark CBS limits. Relative energies for oxygen-/sulfur-containing systems fully characterized with DFT are quite unreliable even with triple-ζ quality basis sets, and 13 out of 45 combinations fortuitously give a relative energy that is within 1kcal mol-1 on average from the benchmark CCSD(T) CBS limit for these systems.

Comparison of the accuracy of DFT methods for reactions with relevance to nitrogenase

We have studied the accuracy of 16 different density functional theory methods to reproduce experimental data for bond lengths, angles, vibrational frequencies, as well as enthalpies and entropies for the binding of N2, H2, CO and hydride ions to various transition-metal complexes (with Fe, Ni, Cr, Mo and W) with relation to nitrogenase. We show that generalized gradient approximation functionals give better structure-related parameters, whereas hybrid functionals often give better energies. However, the BLYP and B97D functionals seem to give reasonably accurate results for both types of properties. Geometries and entropies are converged with split-valence basis sets, but energies and vibrational frequencies (and therefore also thermal corrections) in general require a basis set of triple-zeta quality. Dispersion corrections are important to obtain accurate energies (contributing by up to 57 kJ mol−1), as well as structures.