Accuracy of Several Wave Function and Density Functional Theory Methods for Description of Noncovalent Interaction of Saturated and Unsaturated Hydrocarbon Dimers

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

A Minimum Quantum Chemistry CCSD(T)/CBS Data Set of Dimeric Interaction Energies for Small Organic Functional Groups: Heterodimers

We extend our previous quantum chemistry calculations of interaction energies for 31 homodimers of small organic functional groups (the SOFG-31 data set) by including 239 heterodimers with monomers selected within the SOFG-31 data set, thus resulting in the SOFG-31+239 data set. The minimum-level theoretical scheme contains (1) the basis set superposition error corrected supermolecule (BSSE-SM) approach for intermolecular interactions; (2) the second-order Møller-Plesset perturbation theory (MP2) with the Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets for the geometry optimization and correlation energy calculations; and (3) the single-point energy calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods for the MP2 energy calibrations. In addition, we have performed a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT) in order to gain chemical insights. That the above procedure cannot be further reduced has been proven to be very crucial for constructing reliable data sets of interaction energies. The calculated CCSD(T)/CBS interaction energy data can serve as a benchmark for testing or training less accurate but more efficient calculation methods, such as the electronic density functional theory. As an application, we employ a segmental SAPT model previously developed for the SOFG-31 data set to predict binding energies of large heterodimer complexes. These model energy "quanta" can be used in coarse-grained molecular dynamics simulations by avoiding large-scale calculations.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

The Adsorption of Small Molecules on the Copper Paddle-Wheel: Influence of the Multi-Reference Ground State

We report a theoretical study of the adsorption of a set of small molecules (C₂H₂, CO, CO₂, O₂, H₂O, CH₃OH, C₂H₅OH) on the metal centers of the “copper paddle-wheel”—a key structural motif of many MOFs. A systematic comparison between DFT of different rungs, single-reference post-HF methods (MP2, SOS–MP2, MP3, DLPNO–CCSD(T)), and multi-reference approaches (CASSCF, DCD–CAS(2), NEVPT2) is performed in order to find a methodology that correctly describes the complicated electronic structure of paddle-wheel structure together with a reasonable description of non-covalent interactions. Apart from comparison with literature data (experimental values wherever possible), benchmark calculations with DLPNO–MR–CCSD were also performed. Despite tested methods show qualitative agreement in the majority of cases, we showed and discussed reasons for quantitative differences as well as more fundamental problems of specific cases.

Exploring the Limits of Second- and Third-Order Møller-Plesset Perturbation Theories for Noncovalent Interactions: Revisiting MP2.5 and Assessing the Importance of Regularization and Reference Orbitals

This work systematically assesses the influence of reference orbitals, regularization, and scaling on the performance of second- and third-order Møller-Plesset perturbation theory wave function methods for noncovalent interactions (NCIs). Testing on 19 data sets (A24, DS14, HB15, HSG, S22, X40, HW30, NC15, S66, AlkBind12, CO2Nitrogen16, HB49, Ionic43, TA13, XB18, Bauza30, CT20, XB51, and Orel26rad) covers a wide range of different NCIs including hydrogen bonding, dispersion, and halogen bonding. Inclusion of potential energy surfaces from different hydrogen bonds and dispersion-bound complexes gauges accuracy for nonequilibrium geometries. Fifteen methods are tested. In notation where nonstandard choices of orbitals are denoted as methods:orbitals, these are MP2, κ-MP2, SCS-MP2, OOMP2, κ-OOMP2, MP3, MP2.5, MP3:OOMP2, MP2.5:OOMP2, MP3:κ-OOMP2, MP2.5:κ-OOMP2, κ-MP3:κ-OOMP2, κ-MP2.5:κ-OOMP2, MP3:ωB97X-V, and MP2.5:ωB97X-V. Furthermore, we compare these methods to the ωB97M-V and B3LYP-D3 density functionals, as well as CCSD. We find that the κ-regularization (κ = 1.45 au was used throughout) improves the energetics in almost all data sets for both MP2 (in 17 out of 19 data sets) and OOMP2 (16 out of 19). The improvement is significant (e.g., the root-mean-square deviation (RMSD) for the S66 data set is 0.29 kcal/mol for κ-OOMP2 versus 0.67 kcal/mol for MP2) and for interactions between stable closed-shell molecules, not strongly dependent on the reference orbitals. Scaled MP3 (with a factor of 0.5) using κ-OOMP2 reference orbitals (MP2.5:κ-OOMP2) provides significantly more accurate results for NCIs across all data sets with noniterative O(N⁶) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.

A minimum quantum chemistry CCSD(T)/CBS dataset of dimeric interaction energies for small organic functional groups

We have performed a quantum chemistry study on the bonding patterns and interaction energies for 31 dimers of small organic functional groups (dubbed the SOFG-31 dataset), including the alkane-alkene-alkyne (6 + 4 + 4 = 14, AAA) groups, alcohol-aldehyde-ketone (4 + 4 + 3 = 11, AAK) groups, and carboxylic acid-amide (3 + 3 = 6, CAA) groups. The basis set superposition error corrected super-molecule approach using the second order Møller-Plesset perturbation theory (MP2) with the Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets has been employed in the geometry optimization and energy calculations. To calibrate the MP2 calculated interaction energies for these dimeric complexes, we perform single-point calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods. In order to gain more physical insights, we also perform a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT). The collection of these CCSD(T)/CBS interaction energy values can serve as a minimum quantum chemistry dataset for testing or training less accurate but more efficient calculation methods. As an application, we further propose a segmental SAPT model based on chemically recognizable segments in a specific functional group. These model interactions can be used to construct coarse-grained force fields for larger molecular systems.

Modified Density Functional Dispersion Correction for Inorganic Layered MFX Compounds (M = Ca, Sr, Ba, Pb and X = Cl, Br, I)

MFX (M = Ca, Ba, Sr, Pb and X = Cl, Br, I) compounds have received considerable attention due to their technological application as X-ray detectors, pressure sensors, and optical data storage materials, when doped with rare-earth ions. MFX compounds belong to the class of layered materials with a tetragonal Matlockite crystal structure, characterized by weakly stacked double-halide layers along the crystallographic c-axis. These layers predominantly determine phase transitions, elastic, and mechanical properties. However, the correct description of the lattice parameter c is a challenge for most standard DFT functionals, which tend to overestimate the lattice parameter c. Because of the weak interactions between the halide layers, dispersion-corrected functionals seem to be a better choice. We investigated 11 different inorganic layered MFX compounds for which experimental data are available, with standard and dispersion-corrected functionals to assess their performance in reproducing the lattice parameter c, structural, and vibrational properties of the MFX compounds. Our results revealed that these functionals do not describe the weak interactions between the halide layers in a balanced way. Therefore, we modified Grimme's popular DFT-D2 dispersion correction scheme in two different ways by (i) replacing the dispersion coefficients and van der Waals radii with those of noble gas atoms or (ii) increasing the van der Waals radii of the MFX atoms up to 40%. Comparison with the available experimental data revealed that the latter approach applied to the PBE (Perdew-Burke-Ernzerhof)-D2 functional with 30% increased van der Waals radii, which we coined PBE-D2* (S_rvdw 1.30) is best suited to fine-tune the description of the weak interlayer interactions in MFX compounds, thus significantly improving the description of their structural, vibrational, and mechanical properties. Work is in progress applying this new, computationally inexpensive scheme to other inorganic layered compounds and periodic systems with weakly stacked layers.

A Linear-Scaling Method for Noncovalent Interactions: An Efficient Combination of Absolutely Localized Molecular Orbitals and a Local Random Phase Approximation Approach

A novel method for the accurate and efficient calculation of interaction energies in weakly bound complexes composed of a large number of molecules is presented. The new ALMO+RPAd method circumvents the prohibitive scaling of coupled cluster singles and doubles while still providing similar accuracy across a diverse range of weakly bound chemical systems. Linear-scaling procedures for the Fock build are given utilizing absolutely localized molecular orbitals (ALMOs), resulting in the a priori exclusion of basis set superposition errors. A bespoke data structure and algorithm using density fitting are described, leading to linear scaling for the storage and computation of the two-electron integrals. Electron correlation is included through a new, linear-scaling pairwise local random phase approximation approach, including exchange interactions, and decomposed into purely dispersive excitations (RPAxd). Collectively, these allow meaningful decomposition of the interaction energy into physically distinct contributions: electrostatic, polarization, charge transfer, and dispersion. Comparison with symmetry-adapted perturbation theory shows good qualitative agreement. Tests on various dimers and the S66 benchmark set demonstrate results within 0.5 kcal mol^-1 of coupled cluster singles and doubles results. On a large cluster of water molecules, we achieve calculations involving over 3500 orbital and 12,000 auxiliary basis functions in under 10 min on a single CPU core.

Ab initio molecular dynamics studies of formic acid dimer colliding with liquid water

Ab initio molecular dynamics simulations of formic acid (FA) dimer colliding with liquid water at 300 K have been performed using density functional theory. The two energetically lowest FA dimer isomers were collided with a water slab at thermal and high kinetic energies up to 68kBT. Our simulations agree with recent experimental observations of nearly a complete uptake of gas-phase FA dimer: the calculated average kinetic energy of the dimers immediately after collision is 5 ± 4% of the incoming kinetic energy, which compares well with the experimental value of 10%. Simulations support the experimental observation of no delayed desorption of FA dimers following initial adsorption. Our analysis shows that the FA dimer forms hydrogen bonds with surface water molecules, where the hydrogen bond order depends on the dimer structure, such that the most stable isomer possesses fewer FA-water hydrogen bonds than the higher energy isomer. Nevertheless, even the most stable isomer can attach to the surface through one hydrogen bond despite its reduced hydrophilicity. Our simulations further show that the probability of FA dimer dissociation is increased by high collision energies, the dimer undergoes isomerization from the higher energy to the lowest energy isomer, and concerted double-proton transfer occurs between the FA monomers. Interestingly, proton transfer appears to be driven by the release of energy arising from such isomerization, which stimulates those internal vibrational degrees of freedom that overcome the barrier of a proton transfer.

Survival of the most transferable at the top of Jacob's ladder: Defining and testing the ωB97M(2) double hybrid density functional

A meta-generalized gradient approximation, range-separated double hybrid (DH) density functional with VV10 non-local correlation is presented. The final 14-parameter functional form is determined by screening trillions of candidate fits through a combination of best subset selection, forward stepwise selection, and random sample consensus (RANSAC) outlier detection. The MGCDB84 database of 4986 data points is employed in this work, containing a training set of 870 data points, a validation set of 2964 data points, and a test set of 1152 data points. Following an xDH approach, orbitals from the ωB97M-V density functional are used to compute the second-order perturbation theory correction. The resulting functional, ωB97M(2), is benchmarked against a variety of leading double hybrid density functionals, including B2PLYP-D3(BJ), B2GPPLYP-D3(BJ), ωB97X-2(TQZ), XYG3, PTPSS-D3(0), XYGJ-OS, DSD-PBEP86-D3(BJ), and DSD-PBEPBE-D3(BJ). Encouragingly, the overall performance of ωB97M(2) on nearly 5000 data points clearly surpasses that of all of the tested density functionals. As a Rung 5 density functional, ωB97M(2) completes our family of combinatorially optimized functionals, complementing B97M-V on Rung 3, and ωB97X-V and ωB97M-V on Rung 4. The results suggest that ωB97M(2) has the potential to serve as a powerful predictive tool for accurate and efficient electronic structure calculations of main-group chemistry.

State-of-the-Art Calculations of Sublimation Enthalpies for Selected Molecular Crystals and Their Computational Uncertainty

A computational methodology for calculation of sublimation enthalpies of molecular crystals from first principles is developed and validated by comparison to critically evaluated literature experimental data. Temperature-dependent sublimation enthalpies for a set of selected 22 molecular crystals in their low-temperature phases are calculated. The computational methodology consists of several building blocks based on high-level electronic structure methods of quantum chemistry and statistical thermodynamics. Ab initio methods up to the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction with an estimated complete basis set description [CCSD(T)/CBS] are used to calculate the cohesive energies of crystalline phases within a fragment-based additive scheme. Density functional theory (DFT) calculations with periodic boundary conditions (PBC) coupled with the quasi-harmonic approximation are used to evaluate the thermal contributions to the enthalpy of the solid phase. The properties of the vapor phase are calculated within the ideal-gas model using the rigid-rotor harmonic-oscillator model with correction for internal rotation using a one-dimensional hindered rotor approximation and a proper treatment of the molecular rotational degrees of freedom in the vicinity of 0 K. All individual terms contributing to the sublimation enthalpy as a function of temperature are discussed and their uncertainties estimated by comparison to critically evaluated experimental data.

Computational methods for the description of pharmacologically relevant platinum complexes--molecular structure and bond dissociation

Cancer is after cardiovascular disease the most frequent cause of death in Europe. In 28 of 53 countries considered in this area it is already the leading cause of death and expected to gain even more importance until the year 2020. Amongst the large arsenal of different anti-cancer drugs, platinum drugs belong to the first developed anticancer drugs and still have a large impact on cancer therapy. Nevertheless therapy with platinum-anticancer drugs is accompanied by severe adverse effects caused by frequent interactions with the amino acids of different human proteins. Computational chemistry offers methods to study such interactions and even those of not yet synthesized drugs in silico. For such studies a profound knowledge of the prediction quality of various computational methods towards platinum-drug-like complexes is necessary. By this article we are aiming on delivering important accuracy information of the frequently used computational methods. Most important findings are the high performance of the double hybrid functional B2PLYP for the calculation of geometries, even in small basis sets, followed by BP86 and PBE and the still acceptable performance of the semi-empirical Method PM6-D3H4X for extremely large systems. To follow absolute energies of the dissociation process, LPNO-CEPA and B3LYP-D3 can be suggested while SCS-MP2 shows an extremely narrow standard deviation and a low maximum error, which make it an ideal candidate for relative energy calculations in the exploration of reaction mechanisms.

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.

CCSD(T)/CBS fragment-based calculations of lattice energy of molecular crystals

A comparative study of the lattice energy calculations for a data set of 25 molecular crystals is performed using an additive scheme based on the individual energies of up to four-body interactions calculated using the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction (CCSD(T)) with an estimated complete basis set (CBS) description. The CCSD(T)/CBS values on lattice energies are used to estimate sublimation enthalpies which are compared with critically assessed and thermodynamically consistent experimental values. The average absolute percentage deviation of calculated sublimation enthalpies from experimental values amounts to 13% (corresponding to 4.8 kJ mol(-1) on absolute scale) with unbiased distribution of positive to negative deviations. As pair interaction energies present a dominant contribution to the lattice energy and CCSD(T)/CBS calculations still remain computationally costly, benchmark calculations of pair interaction energies defined by crystal parameters involving 17 levels of theory, including recently developed methods with local and explicit treatment of electronic correlation, such as LCC and LCC-F12, are also presented. Locally and explicitly correlated methods are found to be computationally effective and reliable methods enabling the application of fragment-based methods for larger systems.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Gas Phase Detection of the NH-P Hydrogen Bond and Importance of Secondary Interactions

We have observed the NH···P hydrogen bond in a gas phase complex. The bond is identified in the dimethylamine-trimethylphosphine complex by a red shift of the fundamental NH-stretching frequency observed using Fourier transform infrared spectroscopy (FT-IR). On the basis of the measured NH-stretching frequency red shifts, we find that P is a hydrogen bond acceptor atom similar in strength to S. Both are stronger acceptors than O and significantly weaker acceptors than N. The hydrogen bond angle, ∠NHP, is found to be very sensitive to the functional employed in density functional theory (DFT) optimizations of the complex and is a possible parameter to assess the quality of DFT functionals. Natural bonding orbital (NBO) energies and results from the topological methods atoms in molecules (AIM) and noncovalent interactions (NCI) indicate that the sensitivity is caused by the weakness of the hydrogen bond compared to secondary interactions. We find that B3LYP favors the hydrogen bond and M06-2X favors the secondary interactions leading to under- and overestimation, respectively, of the hydrogen bond angle relative to a DF-LCCSD(T)-F12a calculated angle. The remaining functionals tested, B3LYP-D3, B3LYP-D3BJ, CAM-B3LYP, and ωB97X-D, as well as MP2, show comparable contributions from the hydrogen bond and the secondary interactions and are close to DF-LCCSD(T)-F12a results.

All-atom molecular dynamics simulations of an artificial sodium channel in a lipid bilayer: the effect of water solvation/desolvation of the sodium ion

All-atom molecular dynamics is used to investigate the transport of Na(+) across a 1,2-dioleoyl-sn-glycero-3-phosphocholine lipid bilayer facilitated by a diazacrown hydraphile. Specifically, the free energy of Na(+) passing through the bilayer is calculated using the adaptive biasing force method to study the free energy associated with the increase in Na(+) transport in the presence of the hydraphile molecule. The results show that water interaction greatly influences Na(+) transport through the lipid bilayer as water is pulled through the bilayer with Na(+) forming a water channel. The hydraphile causes a reduction in the free energy barrier for the transport of Na(+) through the head group part of the lipid bilayer since it complexes the Na(+) reducing the necessity for water to be complexed and, therefore, dragged through with Na(+), an energetically unfavorable process. The free energy associated with Na(+) being desolvated within the bilayer is significantly decreased in the presence of the hydraphile molecule; the hydraphile increases the number of solvation states of Na(+) that can be adopted, and this increase in the number of available configurations provides an entropic explanation for the success of the hydraphile.

Understanding the fundamental role of π/π, σ/σ, and σ/π dispersion interactions in shaping carbon-based materials

Noncovalent interactions involving aromatic rings, such as π-stacking and CH/π interactions, are central to many areas of modern chemistry. However, recent studies proved that aromaticity is not required for stacking interactions, since similar interaction energies were computed for several aromatic and aliphatic dimers. Herein, the nature and origin of π/π, σ/σ, and σ/π dispersion interactions has been investigated by using dispersion-corrected density functional theory, energy decomposition analysis, and the recently developed noncovalent interaction (NCI) method. Our analysis shows that π/π and σ/σ stacking interactions are equally important for the benzene and cyclohexane dimers, explaining why both compounds have similar boiling points. Also, similar dispersion forces are found in the benzene⋅⋅⋅methane and cyclohexane⋅⋅⋅methane complexes. However, for systems larger than naphthalene, there are enhanced stacking interactions in the aromatic dimers adopting a parallel-displaced configuration compared to the analogous saturated systems. Although dispersion plays a decisive role in stabilizing all the complexes, the origin of the π/π, σ/σ, and σ/π interactions is different. The NCI method reveals that the dispersion interactions between the hydrogen atoms are responsible for the surprisingly strong aliphatic interactions. Moreover, whereas σ/σ and σ/π interactions are local, the π/π stacking are inherently delocalized, which give rise to a non-additive effect. These new types of dispersion interactions between saturated groups can be exploited in the rational design of novel carbon materials.

Accelerating MP2C dispersion corrections for dimers and molecular crystals

The MP2C dispersion correction of Pitonak and Hesselmann [J. Chem. Theory Comput. 6, 168 (2010)] substantially improves the performance of second-order Møller-Plesset perturbation theory for non-covalent interactions, albeit with non-trivial computational cost. Here, the MP2C correction is computed in a monomer-centered basis instead of a dimer-centered one. When applied to a single dimer MP2 calculation, this change accelerates the MP2C dispersion correction several-fold while introducing only trivial new errors. More significantly, in the context of fragment-based molecular crystal studies, combination of the new monomer basis algorithm and the periodic symmetry of the crystal reduces the cost of computing the dispersion correction by two orders of magnitude. This speed-up reduces the MP2C dispersion correction calculation from a significant computational expense to a negligible one in crystals like aspirin or oxalyl dihydrazide, without compromising accuracy.

The accuracy of quantum chemical methods for large noncovalent complexes

We evaluate the performance of the most widely used wavefunction, density functional theory, and semiempirical methods for the description of noncovalent interactions in a set of larger, mostly dispersion-stabilized noncovalent complexes (the L7 data set). The methods tested include MP2, MP3, SCS-MP2, SCS(MI)-MP2, MP2.5, MP2.X, MP2C, DFT-D, DFT-D3 (B3-LYP-D3, B-LYP-D3, TPSS-D3, PW6B95-D3, M06-2X-D3) and M06-2X, and semiempirical methods augmented with dispersion and hydrogen bonding corrections: SCC-DFTB-D, PM6-D, PM6-DH2 and PM6-D3H4. The test complexes are the octadecane dimer, the guanine trimer, the circumcoronene…adenine dimer, the coronene dimer, the guanine-cytosine dimer, the circumcoronene…guanine-cytosine dimer, and an amyloid fragment trimer containing phenylalanine residues. The best performing method is MP2.5 with relative root mean square deviation (rRMSD) of 4 %. It can thus be recommended as an alternative to the CCSD(T)/CBS (alternatively QCISD(T)/CBS) benchmark for molecular systems which exceed current computational capacity. The second best non-DFT method is MP2C with rRMSD of 8 %. A method with the most favorable "accuracy/cost" ratio belongs to the DFT family: BLYP-D3, with an rRMSD of 8 %. Semiempirical methods deliver less accurate results (the rRMSD exceeds 25 %). Nevertheless, their absolute errors are close to some much more expensive methods such as M06-2X, MP2 or SCS(MI)-MP2, and thus their price/performance ratio is excellent.

Corrected small basis set Hartree-Fock method for large systems

A quantum chemical method based on a Hartree-Fock calculation with a small Gaussian AO basis set is presented. Its main area of application is the computation of structures, vibrational frequencies, and noncovalent interaction energies in huge molecular systems. The method is suggested as a partial replacement of semiempirical approaches or density functional theory (DFT) in particular when self-interaction errors are acute. In order to get accurate results three physically plausible atom pair-wise correction terms are applied for London dispersion interactions (D3 scheme), basis set superposition error (gCP scheme), and short-ranged basis set incompleteness effects. In total nine global empirical parameters are used. This so-called Hartee-Fock-3c (HF-3c) method is tested for geometries of small organic molecules, interaction energies and geometries of noncovalently bound complexes, for supramolecular systems, and protein structures. In the majority of realistic test cases good results approaching large basis set DFT quality are obtained at a tiny fraction of computational cost.

Filled and Empty Orbital Interactions in a Planar Covalent Organic Framework on Graphene

The electronic characteristics of a planar covalent organic framework (COF) on graphene are investigated by means of dispersion-corrected density functional theory. The aromatic central molecule of the COF acts as an electron donor to graphene, while the linker of the COF acts as an electron acceptor. The concerted interaction between the filled orbitals of the central molecule and empty orbitals of the linker promotes the formation of planar COF networks on graphene. The calculation results are in very good agreement with experimental findings of an ordered hexagonal and square COF planar on graphene, which sheds light on the supermolecular assembly mechanism.