Minnesota Density Functionals Research Articles

Origins of the unphysical noncovalent interaction energy curves obtained with the 2011 and 2012 Minnesota density functionals.

With the noncovalent interaction energy curves of the methane dimer [(CH4)2], we have clarified two different origins of the unphysical noncovalent interaction energy curves obtained with the Minnesota density functionals of M11-L, MN12-L, and MN12-SX. For the M11-L functional, the unphysical inflection point on the (CH4)2 interaction energy curve originates from the inclusion of the long-range exchange. As to the MN12-L and MN12-SX functionals, the lack of smoothness restraints results in unphysical inflection points on the corresponding (CH4)2 interaction energy curves. As a result, exchange functionals are as important as dispersion corrections for density functionals to map noncovalent interaction energy surfaces reasonably. Moreover, very highly parameterized functionals with smoothness restraints are suggested for investigating noncovalent interaction energy surfaces.

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder.

The accurate representation of the structural and dynamical properties of water is essential for simulating the unique behavior of this ubiquitous solvent. Here we assess the current status of describing liquid water using ab initio molecular dynamics, with a special focus on the performance of all the later generation Minnesota functionals. Findings are contextualized within the current knowledge on DFT for describing bulk water under ambient conditions and compared to experimental data. We find that, contrary to the prevalent idea that local and semilocal functionals overstructure water and underestimate dynamical properties, M06-L, revM06-L, and M11-L understructure water, while MN12-L and MN15-L overdistance water molecules due to weak cohesive effects. This can be attributed to a weakening of the hydrogen bond network, which leads to dynamical fingerprints that are over fast. While most of the hybrid Minnesota functionals (M06, M08-HX, M08-SO, M11, MN12-SX, and MN15) also yield understructured water, their dynamical properties generally improve over their semilocal counterparts. It emerges that exact exchange is a crucial component for accurately describing hydrogen bonds, which ultimately leads to corrections in both the dynamical and structural properties. However, an excessive amount of exact exchange strengthens hydrogen bonds and causes overstructuring and slow dynamics (M06-HF). As a compromise, M06-2X is the best performing Minnesota functional for water, and its D3 corrected variant shows very good structural agreement. From previous studies considering nuclear quantum effects (NQEs), the hybrid revPBE0-D3, and the rung-5 RPA (RPA@PBE) have been identified as the only two approximations that closely agree with experiments. Our results suggest that the M06-2X(-D3) functionals have the potential to further improve the reproduction of experimental properties when incorporating NQEs through path integral approaches. This work provides further proof that accurate modeling of water interactions requires the inclusion of both exact exchange and balanced (non-local) correlation, highlighting the need for higher rungs on Jacob's ladder to achieve predictive simulations of complex biological systems in aqueous environments.

Can Density Functional Theory Be Trusted for High-Order Electric Properties? The Case of Hydrogen-Bonded Complexes.

This work reports on an extensive assessment of the performance of a wide palette of density functional approximations in predicting the (high-order) electric properties of hydrogen-bonded complexes. To this end, we compute the electronic and vibrational contributions to the electric polarizability and the first and second hyperpolarizabilities, using the CCSD(T)/aug-cc-pVTZ level of theory as reference. For all the studied properties, the average absolute errors below 20% can only be obtained using the CAM-B3LYP functional, while LC-BLYP and MN15 are shown to be only slightly less accurate (average absolute errors not exceeding 30%). Among Minnesota density functionals, i.e., M06, M06-2X, and MN15, we only recommend the latter one, which quite accurately predicts the electronic and vibrational (hyper)polarizabilities. We also analyze the optimal tuning of the range-separation parameter μ for the LC-BLYP functional, finding that this approach does not bring any systematic improvement in the predictions of electronic and vibrational (hyper)polarizabilities and the accuracy of computed properties is largely system-dependent. Finally, we report huge errors in predicting the vibrational second hyperpolarizability by ωB97X, M06, and M06-2X functionals. Based on the explicit evaluation of anharmonic terms contributing to the second hyperpolarizability, this failure is traced down to a poor determination of third- and fourth-order energy derivatives with respect to normal modes. These results reveal serious flaws of some density functional approximations and suggest caution in selecting the appropriate functional to calculate not only electronic and vibrational (hyper)polarizabilities but also other molecular properties that contain vibrational anharmonic contributions.

Theoretical prediction of valence and Rydberg excited states: Minnesota exchange‐correlation functionals vs symmetry adapted cluster‐configuration interaction

AbstractDuring this contribution, we present a benchmark investigation on the applicability of several Minnesota functionals from various classes like local meta‐generalized and meta‐nonseparable gradient approximations, hybrids, and range‐separated hybrids for describing the valence and Rydberg excitation energies of some organic compounds from different categories. Furthermore, the performances of Minnesota density functionals from density functional theory are also assessed against a wave function theory based approach in the context of excite states calculations, symmetry adapted cluster‐configuration interaction (SAC‐CI) method. Pragmatically, the singles and doubles linked excitation operators are considered in the SAC‐CI wave functions. With more or less different accountabilities of the considered methods, it is shown that the M06‐2X, M05‐2X, and M11 functionals have the best performances for valence excited states. On the other hand, for Rydberg excited states although the SAC‐CI method outperforms others, the statistical analyses reveal that the efficiency of some Minnesota functionals is also respectable.

How reliable are Minnesota density functionals for modeling phosphorus–hydrogen NMR spin–spin coupling constants?

The Minnesota density functionals may be considered as the widely adopted of the developed functionals between the years 2005 and 2017. In this work, we present a systematic benchmark study on the accountability of several Minnesota functionals for predicting the nuclear magnetic resonance (NMR) spin–spin coupling constants (SSCCs) in diverse sets of compounds containing phosphorus–hydrogen (P–H) bonds for which experimental data were available. Although each of the Minnesota functionals has pros and cons, we find that the local (M06-L), hybrid (M06-2X), and screened exchange (MN12-SX) functionals not only give an improved description of P–H SSCCs with respect to other approximations, but also provide the results better than or comparable to those obtained using other functionals from various rungs. Furthermore, we figure out that the long-range corrected Minnesota functionals are more appropriate for the compounds with P(III), while for the molecules containing P(V) with different geometries the corresponding screened exchange versions are better choices. Perusing the role of continuum solvent versus gas phase shows that the relative rankings of the benchmarked functionals do not generally vary. All in all, the strengths and weaknesses of the Minnesota density functionals aside, hopefully such efforts can pave the way for further improvements on these approximations toward designing novel functionals for modeling various parameters in computational NMR spectroscopy.

How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne6+, and Ne8+?

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study suggested that functionals with few parameters provide more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne6+, and Ne8+ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science 2017, 355, 49-52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. In addition, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.

The effects of different Minnesota functionals on the sensitivity of boron nitride nanocluster to nitrogen dioxide

We investigated the effect of Minnesota density functionals on the NO2 adsorption behavior on the B12N12 nanocluster. Functionals with a large %HF (Hartree-Fock) exchange fail to predict the electronic properties well, giving large values (9.59 and 12.46eV for M06-2X and M06-HF) for the HOMO-LUMO gap (Eg) of the B12N12 cluster compared to the experimental ones (∼5–7eV). The NO2 adsorption energy and Eg are exponentially and linearly increased by going from M06-L with zero %HF to M06-HF with 100% HF exchange, respectively. Electronic sensitivity (S) of the B12N12 is as follows: SM06-L>SM06>SM06-2X>SM06-HF.

Conceptual DFT Descriptors of Amino Acids with Potential Corrosion Inhibition Properties Calculated with the Latest Minnesota Density Functionals.

Amino acids and peptides have the potential to perform as corrosion inhibitors. The chemical reactivity descriptors that arise from Conceptual DFT for the twenty natural amino acids have been calculated by using the latest Minnesota family of density functionals. In order to verify the validity of the calculation of the descriptors directly from the HOMO and LUMO, a comparison has been performed with those obtained through ΔSCF results. Moreover, the active sites for nucleophilic and electrophilic attacks have been identified through Fukui function indices, the dual descriptor Δf(r) and the electrophilic and nucleophilic Parr functions. The results could be of interest as a starting point for the study of large peptides where the calculation of the radical cation and anion of each system may be computationally harder and costly.

A Molecular Electron Density Theory Study of the Chemical Reactivity of Cis- and Trans-Resveratrol.

The chemical reactivity of resveratrol isomers with the potential to play a role as inhibitors of the nonenzymatic glycation of amino acids and proteins, both acting as antioxidants and as chelating agents for metallic ions such as Cu, Al and Fe, have been studied by resorting to the latest family of Minnesota density functionals. The chemical reactivity descriptors have been calculated through Molecular Electron Density Theory encompassing Conceptual DFT. The active sites for nucleophilic and electrophilic attacks have been chosen by relating them to the Fukui function indices, the dual descriptor and the electrophilic and nucleophilic Parr functions. The validity of “Koopmans’ theorem in DFT” has been assessed by means of a comparison between the descriptors calculated through vertical energy values and those arising from the HOMO and LUMO values.

How Accurate Are the Minnesota Density Functionals for Noncovalent Interactions, Isomerization Energies, Thermochemistry, and Barrier Heights Involving Molecules Composed of Main-Group Elements?

The 14 Minnesota density functionals published between the years 2005 and early 2016 are benchmarked on a comprehensive database of 4986 data points (84 data sets) involving molecules composed of main-group elements. The database includes noncovalent interactions, isomerization energies, thermochemistry, and barrier heights, as well as equilibrium bond lengths and equilibrium binding energies of noncovalent dimers. Additionally, the sensitivity of the Minnesota density functionals to the choice of basis set and integration grid is explored for both noncovalent interactions and thermochemistry. Overall, the main strength of the hybrid Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., M06-2X), barrier heights (e.g., M08-HX, M08-SO, MN15), and systems heavily characterized by self-interaction error (e.g., M06-2X, M08-HX, M08-SO, MN15), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-2X is recommended from the 10 hybrid Minnesota functionals). Similarly, the main strength of the local Minnesota density functionals is that the best ones provide very good performance for thermochemistry (e.g., MN15-L), barrier heights (e.g., MN12-L), and systems heavily characterized by self-interaction error (e.g., MN12-L and MN15-L), while the main weakness is that none of them are state-of-the-art for the full spectrum of noncovalent interactions and isomerization energies (although M06-L is clearly the best from the four local Minnesota functionals). As an overall guide, M06-2X and MN15 are perhaps the most broadly useful hybrid Minnesota functionals, while M06-L and MN15-L are perhaps the most broadly useful local Minnesota functionals, although each has different strengths and weaknesses.

Treating London-Dispersion Effects with the Latest Minnesota Density Functionals: Problems and Possible Solutions.

It is shown that the latest Minnesota density functionals (SOGGA11, M11-L, N12, MN12-L, SOGGA11-X, M11, N12-SX, and MN12-SX) do not properly describe London-dispersion interactions. Grimme's DFT-D3 correction can solve this problem partially; however, double-counting of medium-range electron correlation can occur. For the related M06-L functional, the alternative VV10 van der Waals kernel is tested, but it experiences similar double-counting. Most functionals give unphysical dissociation curves for the argon dimer, an indication for method-inherent problems, and further investigation is recommended. These results are further evidence that the London-dispersion problem in density functional theory approximations is unlikely to be solved by mere empirical optimization of functional parameters, unless the functionals contain components that ensure the correct asymptotic long-range behavior. London dispersion is ubiquitous, which is why the reported findings are not only important for theoreticians but also a reminder to the general chemist to carefully consider their choice of method before undertaking computational studies.

Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics

Kohn-Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange-correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading--as a long-range goal--to a functional with good accuracy for all problems, i.e. a universal functional. To guide our path towards that goal and to measure our progress, we have developed-building on earlier work of our group-a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes, such as atomization, complexation, proton addition and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For this paper, we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test two wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore, the results provide a status report on the quest for a universal functional.

Characterizing and Understanding the Remarkably Slow Basis Set Convergence of Several Minnesota Density Functionals for Intermolecular Interaction Energies.

For a set of eight equilibrium intermolecular complexes, it is discovered that the basis set limit (BSL) cannot be reached by aug-cc-pV5Z for three of the Minnesota density functionals: M06-L, M06-HF, and M11-L. In addition, the M06 and M11 functionals exhibit substantial, but less severe, difficulties in reaching the BSL. By using successively finer grids, it is demonstrated that this issue is not related to the numerical integration of the exchange-correlation functional. In addition, it is shown that the difficulty in reaching the BSL is not a direct consequence of the structure of the augmented functions in Dunning's basis sets, since modified augmentation yields similar results. By using a very large custom basis set, the BSL appears to be reached for the HF dimer for all of the functionals. As a result, it is concluded that the difficulties faced by several of the Minnesota density functionals are related to an interplay between the form of these functionals and the structure of standard basis sets. It is speculated that the difficulty in reaching the basis set limit is related to the magnitude of the inhomogeneity correction factor (ICF) of the exchange functional. A simple modification of the M06-L exchange functional that systematically reduces the basis set superposition error (BSSE) for the HF dimer in the aug-cc-pVQZ basis set is presented, further supporting the speculation that the difficulty in reaching the BSL is caused by the magnitude of the exchange functional ICF. Finally, the BSSE is plotted with respect to the internuclear distance of the neon dimer for two of the examined functionals.

Performance of the Widely Used Minnesota Density Functionals for the Prediction of Heat of Formations, Ionization Potentials of Some Benchmarked First Row Transition Metal Complexes

We have computed and investigated the performance of Minnesota density functionals especially the M05, M06, and M08 suite of complementary density functionals for the prediction of the heat of formations (HOFs) and the ionization potentials (IPs) of various benchmark complexes containing nine different first row transition metals. The eight functionals of M0X family, namely, the M05, M05-2X, M06-L, M06, M06-2X, M06-HF, M08-SO, and M08-HX are taken for the computation of the above-mentioned physical properties of such metal complexes along with popular Los Alamos National Laboratory 2 double-ζ (LANL2DZ) basis set. Total 54 benchmark systems are taken for HOF calculation, whereas the 47 systems among these benchmark complexes are chosen for the calculation of IPs because of lack of experimental results on rest of the seven systems. The computed values of HOFs and IPs are compared with the experimental results obtained from the literature. The deviation of these computed values from the actual experimental results is calculated for each eight different M0X functionals to judge their performances in evaluating these properties. Finally, a clear relationship between the exchange correlation energy of eight M0X functionals and their efficiency are made to predict the different physical properties.

Oxygen Interactions with Silica Surfaces: Coupled Cluster and Density Functional Investigation and the Development of a New ReaxFF Potential

We consider oxygen interactions with realistic silica surfaces, including both experimentally observed nondefective surface reconstructions and experimentally observed surface defects. Nondefective models include clusters representing the site above a fully coordinated surface Si atom and bridging O atoms, and the defective models include clusters representing an under-coordinated Si defect, a nonbridging O defect, and a ring structure. Energies were obtained for the approach of atomic and molecular oxygen to these clusters in various configurations by using explicitly correlated CCSD(T)-F12b electronic structure theory and the Minnesota density functionals, which were found to be in good agreement. The Minnesota functionals were employed in binding energy calculations for all of the clusters, considering the singlet and triplet spin states for nondefective clusters and doublet and quartet spin states for defective clusters. We find that the chosen defects are energetically favorable sites for binding. The density functional energies were used to extend the empirical ReaxFFSiO potential for silica, which was previously parametrized for bulk silica polymorphs (van Duin et al. J. Phys. Chem. A, 2003, 107, 3803–3811), to model the gas–surface interactions represented by the defective and nondefective clusters presented here. Interaction energy predictions from ReaxFFSiOGSI agree very well with the density functional energies. ReaxFFSiOGSI can now be employed in reactive large-scale molecular dynamics simulations involving oxygen–silica gas–surface interactions such as oxide growth and the heterogeneous recombination of oxygen occurring on real silica surfaces.

Verdict: Time-Dependent Density Functional Theory “Not Guilty” of Large Errors for Cyanines

We assess the accuracy of eight Minnesota density functionals (M05 through M08-SO) and two others (PBE and PBE0) for the prediction of electronic excitation energies of a family of four cyanine dyes. We find that time-dependent density functional theory (TDDFT) with the five most recent of these functionals (from M06-HF through M08-SO) is able to predict excitation energies for cyanine dyes within 0.10-0.36 eV accuracy with respect to the most accurate available Quantum Monte Carlo calculations, providing a comparable accuracy to the latest generation of CASPT2 calculations, which have errors of 0.16-0.34 eV. Therefore previous conclusions that TDDFT cannot treat cyanine dyes reasonably accurately must be revised.

Stacking and H-bonding patterns of dGpdC and dGpdCpdG: Performance of the M05-2X and M06-2X Minnesota density functionals for the single strand DNA

The Minnesota density functionals, M05-2X and M06-2X, were used to predict the structures of the nucleotide oligomers. This study indicates that these functionals are able to reliable predict bases stacked structures in nucleotide oligomers (dGpdC and dGpdCpdG). The obtained results are in excellent agreement with those from the MP2 theory. The electron density distributions between the stacked nucleobases calculated by the Minnesota density functionals are very close to that evaluated by the MP2 method (differences are less than 0.001 au). The M05-2X and M06-2X functionals also appear to provide a reliable description for the intra-strand H-bonding in single strands of DNA.

How Well Can Modern Density Functionals Predict Internuclear Distances at Transition States?

We introduce a new database called TSG48 containing 48 transition state geometrical data (in particular, internuclear distances in transition state structures) for 16 main group reactions. The 16 reactions are the 12 reactions in the previously published DBH24 database (which includes hydrogen transfer reactions, heavy-atom transfer reactions, nucleophilic substitution reactions, and association reactions plus one unimolecular isomerization) plus four H-transfer reactions in which a hydrogen atom is abstracted by the methyl or hydroperoxyl radical from the two different positions in methanol. The data in TSG48 include data for four reactions that have previously been treated at a very high level in the literature. These data are used to test and validate methods that are affordable for the entire test suite, and the most accurate of these methods is found to be the multilevel BMC-CCSD method. The data that constitute the TSG48 database are therefore taken to consist of these very high level calculations for the four reactions where they are available and BMC-CCSD calculations for the other 12 reactions. The TSG48 database is used to assess the performance of the eight Minnesota density functionals from the M05-M08 families and 26 other high-performance and popular density functionals for locating transition state geometries. For comparison, the MP2 and QCISD wave function methods have also been tested for transition state geometries. The MC3BB and MC3MPW doubly hybrid functionals and the M08-HX and M06-2X hybrid meta-GGAs are found to have the best performance of all of the density functionals tested. M08-HX is the most highly recommended functional due to the excellent performance for all five subsets of TSG48, as well as having a lower cost when compared to doubly hybrid functionals. The mean absolute errors in transition state internuclear distances associated with breaking and forming bonds as calculated by the B2PLYP, MP2, and B3LYP methods are respectively about 2, 3, and 5 times larger than those calculated by MC3BB and M08-HX.

Applications and validations of the Minnesota density functionals

We discuss and review selected recent applications and validations of the Minnesota density functionals, especially the M06 family, emphasizing nanochemistry, organic, inorganic, and biological chemistry, and catalysis and highlighting the broad accuracy of these functionals as compared to previous popular functionals for thermochemistry, kinetics, and noncovalent interactions.

The Minnesota Density Functionals and their Applications to Problems in Mineralogy and Geochemistry

Quantum mechanical electronic structure calculations are playing an increasingly useful role in many areas of mineralogy and geochemistry. This review introduces the density functional method for such calculations, gives an overview of the density functionals developed at the University of Minnesota, and summarizes selected applications using these density functionals that are relevant to mineralogy and geochemistry. A key reason for the importance of computational methods in mineralogy is the ability to explore problems that cannot easily be studied in the laboratory. For example, it is very difficult to carry out laboratory studies under the real conditions of the Earth’s mantle and core because the temperature of the Earth’s core ranges up to 6000 K, and the pressure ranges up to 360 GPa. In the past decade, applications of quantum mechanical methods to understanding the properties of minerals and melts in the Earth’s interior have become increasingly important (Warren and Ackland 1996; Oganov and Brodholt 2000; Stixrude and Peacor 2002; Brodholt and Vocadlo 2006; Gillan et al. 2006; Tsuchiya et al. 2006). Some specific examples of problems in solid-state geochemistry where electronic structure calculations can be particularly useful are phase equilibria (Tsuchiya et al. 2004; Lay et al. 2005; Schwegler et al. 2008), equations of state, elastic constants, bulk and shear moduli (Li et al. 2006), hydrogen, proton, and water diffusion in minerals (Sakamura et al. 2003; Belonoshko et al. 2004; Pohlmann et al. 2004), the character and structural properties of hydroxyl groups in minerals and structures of hydrous minerals (Winkler et al. 1994, 1995; Nobes et al. 2000; Brodholt and Refson 2000; Churakov et al. 2003; Walker et al. 2006; Ockwig et al. 2009), hydrolysis and dissolution mechanisms (Strandh et al. 1997, Criscenti et …