van der Waals corrections to density functional theory calculations: Methane, ethane, ethylene, benzene, formaldehyde, ammonia, water, PBE, and CPMD

Intermolecular π/π and H/π interactions in dimers researched by different computational methods

The analysis of π/π and H /π interactions in complexes are a challenging aspect of theoretical research. Due to the different approximations of different levels of theory, results tend to be inconsistent. We compared the reliabilities of HF, SVWN, M06L, PW91, BLYP, B3LYP, BHandHLYP, B97D, MP2, and DFTB-D approaches in researching π/π and H /π interactions by calculating the binding energies of five benzene-containing dimers. The effects of 6-31+G**, 6-311++G** and 6-311++G(2df,2p) basis sets on the results were analyzed too. We found that the DFTB-D and B97D methods combined with the 6-311++G** basis set perform well for dimers that contain π/π and H /π interactions. With high efficiency and satisfactory precision, DFTB-D is helpful for the calculation of complexes containing π/π and H /π stacking. We further calculated the structures and properties of phenylalanine-containing dimers using the DFTB-D and B97D methods. The properties of low energy conformers such as rotational constants, dipole moments and molecular orbitals were also analyzed. These data should be helpful for research into systems that contain π/π and H /π stacking.

Hydration structure of salt solutions from ab initio molecular dynamics

The solvation structures of Na(+), K(+), and Cl(-) ions in aqueous solution have been investigated using density functional theory (DFT) based Car-Parrinello (CP) molecular dynamics (MD) simulations. CPMD trajectories were collected for systems containing three NaCl or KCl ion pairs solvated by 122 water molecules using three different but commonly employed density functionals (BLYP, HCTH, and PBE) with electron correlation treated at the level of the generalized gradient approximation (GGA). The effect of including dispersion forces was analyzed through the use of an empirical correction to the DFT-GGA scheme. Special attention was paid to the hydration characteristics, especially the structural properties of the first solvation shell of the ions, which was investigated through ion-water radial distribution functions, coordination numbers, and angular distribution functions. There are significant differences between the present results obtained from CPMD simulations and those provided by classical MD based on either the CHARMM force field or a polarizable model. Overall, the computed structural properties are in fair agreement with the available experimental results. In particular, the observed coordination numbers 5.0-5.5, 6.0-6.4, and 6.0-6.5 for Na(+), K(+), and Cl(-), respectively, are consistent with X-ray and neutron scattering studies but differ somewhat from some of the many other recent computational studies of these important systems. Possible reasons for the differences are discussed.

Electronically coarse-grained model for water

We introduce an electronically coarse-grained description of water representing all long range, many-body electronic responses via an embedded quantum oscillator. Leading-order response coefficients and gas phase electrostatic moments are exactly reproduced. Molecular dynamics, using electronic path integral sampling, shows that this framework is sufficient for a realistic liquid to emerge naturally with transferability extending further to nonambient state points and to the free water surface. The model allows the strength of many-body dispersion and polarization to be adjusted independently and these are found to have significant effects on the condensed phase.

Predicting anisotropic displacement parameters using molecular dynamics: density functional theory plus dispersion modelling of thermal motion in benzophenone

The benefits of combining experimental and computational methods have been demonstrated by a study of the dynamics and solid-state structure of α-benzophenone. Dispersion-corrected and -uncorrected density functional theory molecular dynamics simulations were used to obtain displacement parameters, with the dispersion-corrected simulations showing good agreement with the experimental neutron and X-ray diffraction values. At 70 K, quantum-nuclear effects resulted in poor values for the hydrogen atoms, but the heavy-atom values still show excellent agreement, suggesting that molecular dynamics simulations can be a useful tool for determining displacement parameters where experimental data are poor or limited.

Intricacies of Describing Weak Interactions Involving Halogen Atoms within Density Functional Theory

In this work we assess the performance of different dispersion-corrected density functional theory (DFT) approaches (M06, M06-2X, DFT-D3, and DCACP) in reproducing high-level wave function based benchmark calculations on the weakly bound halogen dimers X2···X2 and X2···Ar (for X = F, Cl, Br, and I), as well as the prototype halogen bonded complexes H3CX···OCH2 (X = Cl, Br, I). In spite of the generally good performance of all tested methods for weakly bound systems, their performance for halogen-containing compounds varies largely. We find maximum errors in the energies with respect to the CCSD(T) reference values of 0.13 kcal/mol for DCACP, 0.22 kcal/mol for M06-2X, 0.47 kcal/mol for BLYP-D3, and 0.77 kcal/mol for M06. The root-mean-square deviations are 0.13 kcal/mol for DCACP and M06-2X, 0.44 kcal/mol for M06, and 0.51 kcal/mol for BLYP-D3.

Ab initio molecular dynamics study of water at constant pressure using converged basis sets and empirical dispersion corrections

It is generally believed that studies of liquid water using the generalized gradient approximation to density functional theory require dispersion corrections in order to obtain reasonably accurate structural and dynamical properties. Here, we report on an ab initio molecular dynamics study of water in the isothermal-isobaric ensemble using a converged discrete variable representation basis set and an empirical dispersion correction due to Grimme [J. Comp. Chem. 27, 1787 (2006)]. At 300 K and an applied pressure of 1 bar, the density obtained without dispersion corrections is approximately 0.92 g/cm(3) while that obtained with dispersion corrections is 1.07 g/cm(3), indicating that the empirical dispersion correction overestimates the density by almost as much as it is underestimated without the correction for this converged basis. Radial distribution functions exhibit a loss of structure in the second solvation shell. Comparison of our results with other studies using the same empirical correction suggests the cause of the discrepancy: the Grimme dispersion correction is parameterized for use with a particular basis set; this parameterization is sensitive to this choice and, therefore, is not transferable to other basis sets.

Molecular vibrations of methane molecules in the structure I clathrate hydrate from ab initio molecular dynamics simulation

Vibrational frequencies of guest molecules in clathrate hydrates reflect the molecular environment and dynamical behavior of molecules. A detailed understanding of the mechanism for the vibrational frequency changes of the guest molecules in the clathrate hydrate cages is still incomplete. In this study, molecular vibrations of methane molecules in a structure I clathrate hydrate are calculated from ab initio molecular dynamics simulation. The vibrational spectra of methane are computed by Fourier transform of autocorrelation functions, which reveal distinct separation of each vibrational mode. Calculated symmetric and asymmetric stretching vibrational frequencies of methane molecules are lower in the large cages than in the small cages (8 and 16 cm(-1) for symmetric and asymmetric stretching, respectively). These changes are closely linked with the C-H bond length. The vibrational frequencies for the bending and rocking vibrational modes nearly overlap in each of the cages.

On the Structure and Geometry of Biomolecular Binding Motifs (Hydrogen-Bonding, Stacking, X-H···π): WFT and DFT Calculations

The strengths of noncovalent interactions are generally very sensitive to a number of geometric parameters. Among the most important of these parameters is the separation between the interacting moieties (in the case of an intermolecular interaction, this would be the intermolecular separation). Most works seeking to characterize the properties of intermolecular interactions are mainly concerned with binding energies obtained at the potential energy minimum (as determined at some particular level of theory). In this work, in order to extend our understanding of these types of noncovalent interactions, we investigate the distance dependence of several types of intermolecular interactions, these are hydrogen bonds, stacking interactions, dispersion interactions, and X-H···π interactions. There are several methods that have traditionally been used to treat noncovalent interactions as well as many new methods that have emerged within the past three or four years. Here we obtain reference data using estimated CCSD(T) values at the complete basis set limit (using the CBS(T) method); potential energy curves are also produced using several other methods thought to be accurate for intermolecular interactions, these are MP2/cc-pVTZ, MP2/aug-cc-pVDZ, MP2/6-31G*(0.25), SCS(MI)-MP2/cc-pVTZ, estimated MP2.5/CBS, DFT-SAPT/aug-cc-pVTZ, DFT/M06-2X/6-311+G(2df,2p), and DFT-D/TPSS/6-311++G(3df,3pd). The basis set superposition error is systematically considered throughout the study. It is found that the MP2.5 and DFT-SAPT methods, which are both quite computationally intensive, produce potential energy curves that are in very good agreement to those of the reference method. Among the MP2 techniques, which can be said to be of medium computational expense, the best results are obtained with MP2/cc-pVTZ and SCS(MI)-MP2/cc-pVTZ. DFT-D/TPSS/6-311++G(3df,3pd) is the DFT-based method that can be said to give the most well-balanced description of intermolecular interactions.

Further analysis and comparative study of intermolecular interactions using dimers from the S22 database

Accurate MP2 and CCSD(T) complete basis set (CBS) interaction energy curves (14 points for each curve) have been obtained for 20 of the dimers reported in the S22 set and analytical Morse curves have been fitted that can be used in developing updated density functional theory (DFT) and force field models. The magnitude and the effect of the basis set superposition error (BSSE) were carefully investigated. We found that going up to aug-cc-pVDZ and aug-cc-pVTZ basis sets is enough to obtain accurate CBS MP2 energies when BSSE corrected values are used but aug-cc-pVTZ and aug-cc-pVQZ basis sets are needed when the BSSE uncorrected total energies are used in CBS extrapolations. MP2 interaction energies with smaller basis sets such as 6-31G* are found to have very little dispersion energy and that the true source of dispersion attributed attractive interactions is almost entirely due to BSSE. MP2 and CCSD(T) CBS interaction energies are found to be very close to one another if aromatic systems are not involved. Comparative analyses have been performed with semiempirical and ab initio methods utilizing the moderate in size but affordable 6-31G* basis set both of which can be readily applied to macromolecular systems. The new M06-2X and M06-L DFT functionals were found to be more accurate than all methods tested herein. Interaction energy curves using the SG1 grid showed discontinuities for several of the dimer systems but this problem disappeared when finer DFT numerical grids were used.

Van der Waals interactions in density functional theory using Wannier functions

van der Waals interactions between atoms and molecules are ubiquitous and very important for many molecular and condensed-matter structures. These systems are often studied from first principles using the density functional theory (DFT), because this approach often represents a good compromise between accuracy and efficiency. However, the commonly used DFT functionals are not able to describe properly van der Waals effects. Most attempts to correct for this problem have a basic semiempirical character, although computationally more expensive first principles schemes have been recently developed. Of course, the key issue is finding a way to include van der Waals interactions in DFT without dramatically increasing the computational cost. We here describe in detail the recently developed scheme, based on the use of the maximally localized Wannier functions, that combines the simplicity of the semiempirical formalism with the accuracy of the first principles approaches and appears to be promising, being simple, efficient, accurate, and transferable (for instance, charge polarization effects are naturally included). The results of successful applications to small molecules, bulk Ar, and the interaction of Ar, He, and H(2) with two different Al surfaces are presented. Directions for further improvements of the method are finally suggested.

Importance of van der Waals interactions in liquid water

We present ab initio molecular dynamics studies on liquid water using density functional theory in conjunction with either dispersion-corrected atom-centered potentials or empirical van der Waals corrections. Our results show that improving the description of van der Waals interactions in DFT-GGA leads to a softening of liquid water's structure with higher mobility. The results obtained with dispersion-corrected atom-centered potentials are especially encouraging. In particular, the radial distribution functions are in better agreement with experiment, and the self-diffusion coefficient increases by more than three-fold compared with the one predicted by the BLYP functional. This work demonstrates that van der Waals interactions are essential in fine-tuning both structural and dynamical properties of liquid water.

Performance of the DFT-D method, paired with the PCM implicit solvation model, for the computation of interaction energies of solvated complexes of biological interest

In this work we investigate the performance of the DFT method, augmented with an empirical dispersion function (DFT-D), paired with the PCM implicit solvation model, for the computation of noncovalent interaction energies of biologically-relevant, solvated model complexes. It is found that this method describes intermolecular interactions within water and ether (protein-like) environments with roughly the same accuracy as in the gas phase. Another important finding is that, when environmental effects are taken into account, the empirical dispersion term associated with the DFT-D method need be modified very little (or not at all), in order to obtain the optimum, most well balanced, performance.

Assessment of the MP2 method, along with several basis sets, for the computation of interaction energies of biologically relevant hydrogen bonded and dispersion bound complexes

In the past several years the MP2 method has been used extensively in studies of noncovalent interactions within biological systems such as proteins, DNA/RNA, and protein-ligand complexes. In this work we assess the performance that can be expected of this method, when paired with several different medium and extended basis sets, for the accurate computation of binding energies of hydrogen bonded and dispersion bound biologically derived complexes. It is found that, overall, the MP2/cc-pVTZ method produces the best, most well balanced, description of noncovalent interactions. Another interesting observation made in this study is that generally the MP2 technique, when paired with any basis set, does not yield reliable results for cyclic hydrogen bonds such as those found in nucleic acid base pairs.