Accurate description of van der Waals complexes by density functional theory including empirical corrections

An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R(-6). The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene. H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies.     

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self‐interaction correction (SIC) used in density functional theory does not remove all self‐interaction. We present as an alternative a novel method that, by construction, is totally free from self‐interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001     

黄酮类化合物的密度泛函理论研究

在混合密度泛函B3LYP理论下,用6-31G*基函数研究了几种典型黄酮类化合物分子的几何结构、电子结构和分子的静电势,讨论了电子结构和分子活性部位的关系.     

Implementation of empirical dispersion corrections to density functional theory for periodic systems

A recently developed empirical dispersion correction (Grimme et al., J. Chem. Phys. 2010, 132, 154104) to standard density functional theory (DFT‐D3) is implemented in the plane‐wave program package VASP. The DFT‐D3 implementation is compared with an implementation of the earlier DFT‐D2 version (Grimme, J. Comput. Chem. 2004, 25, 1463; Grimme, J. Comput. Chem. 2006, 27, 1787). Summation of empirical pair potential terms is performed over all atom pairs in the reference cell and over atoms in shells of neighboring cells until convergence of the dispersion energy is obtained. For DFT‐D3, the definition of coordination numbers has to be modified with respect to the molecular version to ensure convergence. The effect of three‐center terms as implemented in the original molecular DFT‐D3 version is investigated. The empirical parameters are taken from the original DFT‐D3 version where they had been optimized for a reference set of small molecules. As the coordination numbers of atoms in bulk and surfaces are much larger than in the reference compounds, this effect has to be discussed. The results of test calculations for bulk properties of metals, metal oxides, benzene, and graphite indicate that the original parameters are also suitable for solid‐state systems. In particular, the interlayer distance in bulk graphite and lattice constants of molecular crystals is considerably improved over standard functionals. With the molecular standard parameters (Grimme et al., J. Chem. Phys. 2010, 132, 154104; Grimme, J. Comput. Chem. 2006, 27, 1787) a slight overbinding is observed for ionic oxides where dispersion should not contribute to the bond. For simple adsorbate systems, such as Xe atoms and benzene on Ag(111), the DFT‐D implementations reproduce experimental results with a similar accuracy as more sophisticated approaches based on perturbation theory (Rohlfing and Bredow, Phys. Rev. Lett. 2008, 101, 266106). © 2012 Wiley Periodicals, Inc.     

Fully ab initio protein‐ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT‐D3) is used for fully ab initio protein‐ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three‐body and higher many‐body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side‐chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full‐system calculation for the 1060 atoms containing PL complex. For charged amino acid side‐chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (? = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (?30 and ?54 kcal/mol). © 2012 Wiley Periodicals, Inc.     

Lennard-Jones parameters for small diameter carbon nanotubes and water for molecular mechanics simulations from van der Waals density functional calculations

Lennard-Jones (LJ) parameters are derived for classical nonpolarizable force fields for carbon nanotubes (CNTs) and for CNT-water interaction from van der Waals (vdW) enhanced density functional calculations. The new LJ parameters for carbon-carbon interactions are of the same order as those previously used in the literature but differ significantly for CNT-water interactions. This may partially originate from the fact that in addition to pure vdW interactions the polarization and other quantum mechanics effects are embedded into the LJ-potential.     

van der Waals interactions are critical in Car–Parrinello molecular dynamics simulations of porphyrin–fullerene dyads

The interplay between electrostatic and van der Waals (vdW) interactions in porphyrin‐C₆₀ dyads is still under debate despite its importance in influencing the structural characteristics of such complexes considered for various applications in molecular photovoltaics. In this article, we sample the conformational space of a porphyrin‐C₆₀ dyad using Car–Parrinello molecular dynamics simulations with and without empirical vdW corrections. Long‐range vdW interactions, which are poorly described by the commonly used density functional theory functionals, prove to be essential for a proper dynamics of the dyad moieties. Inclusion of vdW corrections brings porphyrin and C₆₀ close together in an orientation that is in agreement with experimental observations. The structural differences arising from the vdW corrections are shown to be significant for several properties and potentially less important for others. Additionally, our Mulliken population analysis reveals that contrary to the common belief, porphyrin is not the primary electron donating moiety for C₆₀. In the considered dyad, fullerene's affinity for electrons is primarily satisfied by charge transfer from the amide group of the linker. However, we show that in the absence of another suitable bound donor, C₆₀ can withdraw electrons from porphyrin if it is sufficiently close. © 2015 Wiley Periodicals, Inc.     

Time‐dependent density functional theory study on direction‐dependent electron and hole transfer processes in molecular systems

We report on real‐time time‐dependent density functional theory calculations on direction‐dependent electron and hole transfer processes in molecular systems. As a model system, we focus on α‐sulfur. It is shown that time scale of the electron transfer process from a negatively charged S₈ molecule to a neighboring neutral monomer is comparable to that of a strong infrared‐active molecular vibrations of the dimer with one negatively charged monomer. This results in a strong coupling between the electrons and the nuclei motion which eventually leads to S₈ ring opening before the electron transfer process is completed. The open‐ring structure is found to be stable. The similar infrared‐active peak in the case of hole transfer, however, is shown to be very weak and hence no significant scattering by the nuclei is possible. The presented approach to study the charge transfer processes in sulfur has direct applications in the increasingly growing research field of charge transport in molecular systems. © 2017 Wiley Periodicals, Inc.     

Analytical gradients for subsystem density functional theory within the slater‐function‐based amsterdam density functional program

We present a new implementation of analytical gradients for subsystem density‐functional theory (sDFT) and frozen‐density embedding (FDE) into the Amsterdam Density Functional program (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are conducted and compared to reference data. Our results confirm that sDFT‐LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 Å) compared to reference wave‐function theory results. However, sDFT‐PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 Å). The flexibility of our new implementation is demonstrated for an HCN‐trimer test system, for which several different setups are applied. © 2016 Wiley Periodicals, Inc.     

氢化可的松的热力学函数和晶体结构——密度泛函理论分析

采用密度泛函理论B3LYP/6-31G和B3LYP/6-311G*方法优化了气相状态氢化可的松的几何结构,利用优化的结构得到了氢化可的松各原子净电荷及前沿轨道分布;基于简谐振动分析求得氢化可的松的红外光谱频率和热力学函数;并计算了环己烷、乙酸丁酯、二氯乙烷、异丙醇、甲醇、水六种不同极性的溶剂对氢化可的松几何构型、电荷分布及能量的影响.结果表明,由理论计算得到的氢化可的松的晶体结构与实测的晶体结构接近.     

A density functional theory-based chemical potential equalisation approach to molecular polarizability

The electron density changes in molecular systems in the presence of external electric fields are modeled for simplicity in terms of the induced charges and dipole moments at the individual atomic sites. A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of density functional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few illustrative numerical calculations are shown to predict the molecular polarizabilities in good agreement with available results. The usefulness of the approach to the calculation of intermolecular interaction needed for computer simulation is highlighted.     

Vibrational corrections to geometries of transition metal complexes from density functional theory

Zero-point vibrational corrections are computed at the BP86/AE1 level for the set of 50 transition-metal/ligand bonds that have recently been proposed as testing ground for DFT methods, because of the availability of precise experimental gas-phase geometries (Bühl and Kabrede, J Chem Theory Comput 2006, 2, 1282). These corrections are indicated to be transferable to a large extent between various density-functional/basis-set combinations, so that they can be used to estimate zero-point averaged r0g distances from re values optimized at other theoretical levels. Applying this approach to a number of popular DFT levels does not, in general, improve their overall accuracy in terms of mean and standard deviations from experiment. The hybrid variant of the meta-functional TPSS is confirmed as promising choice for computing structures of transition-metal complexes.     

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

Parameters are developed for a practical application of the empirical van der Waals (vdW) correction infrastructure available in the CPMD density functional theory (DFT) code. The binding energy, geometry, and potential energy surface (PES) are examined for methane, ethane, ethylene, formaldehyde, ammonia, three benzene dimer geometries, and three benzene–water geometries. The vdW corrected results compare favorably with MP2 and CCSD(T) calculations near the complete basis set limits, and with experimental results where they are available.     

From orientation disordered to ordered—An ab initio simulation on ammonia borane phase transition within van der Waals corrections

In this work, we report a detailed theoretical investigation of the phase transition of ammonia borane (NH₃BH₃; AB), from a tetragonal I4mm ( ) phase with disordered orientation of hydrogen to an orthorhombic phase with Pmn2₁ ( ) symmetry, as a function of temperature based on Density Functional Theory calculations with semiempirical dispersion potential correction. We define a series of substructures with the NH₃BH₃ moiety always in C_3v symmetry and the partially occupied high temperature state can be described as a continuous transformation between these substructures. To understand the role of the van der Waals corrections to the physical properties, we use the empirical Grimme's dispersion potential correction (PBE‐D2). Both Perdew–Burke–Emzerhof (PBE) and PBE‐D2 functional yield almost the same energy sequence along the transition path. However, PBE‐D2 functional shows obvious advantage in describing the lattice parameters of AB. The rigid rotor harmonic oscillator approximation is used to compute the free energy and the entropies contribution along the transition pathway. With knowledge of free energy surfaces along rotations of the ? [NH₃] and ? [BH₃] groups, complete transformation paths are mapped out. The phase transition is found to follow the sequence of partially occupied tetragonal system (I4mm) of a mixture of states with monoclinic (Cc), (CM) and orthorhombic (Pmn2₁) symmetries to fully occupied quasitetragonal system (the intermediate phase, Pmn2₁) to fully occupied orthorhombic system (Pmn2₁). © 2014 Wiley Periodicals, Inc.     

First‐order correlation‐kinetic contribution to Kohn–Sham exchange charge density function in atoms,using quantal density functional theory approach

Using the static exchange‐correlation charge density concept, the total integrated exchange‐charge density function is calculated within the nonrelativistic spin‐restricted exchange‐only (i) optimized effective potential model, and (ii) nonvariational local potential derived from the exchange‐only work potential within the quantal density functional theory, for the ground‐state isoelectronic series: Ga⁺, Zn, Cu^?; In⁺, Cd, Ag^?; and Tl⁺, Hg, Au^?. The difference between the exchange charge density function derived from these potentials is employed to evaluate the first‐order correlation‐kinetic contribution to the integrated exchange charge density. This contribution is found to be important for both the intra‐ and inter‐shell regions. Screening effects on the contribution due to the nd¹⁰ (n = 3–5) subshells are discussed through comparisons with similar calculations on Ca, Sr, and Ba, wherein nd¹⁰ electrons are absent. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Exchange and correlation in density functional theory and quantum chemistry

The nature of exchange, dynamic correlation (DC) and left–right correlation (LRC) is considered in density functional theory and wavefunction‐based quantum chemistry. The presence of LRC in approximate exchange density functionals is highlighted and the separation of LRC and DC is considered. For H₂, the Heitler–London approach is shown to include the essential elements of exchange and LRC. The arguments are illustrated by a comparison of Gaussian orbital s‐optimised Heitler–London and OPTX potential energy curves. They agree well near equilibrium, but differ at large distances due to the inability of the OPTX form to describe the dissociation process. LRC and DC values determined using the two approaches are compared. The influence of higher angular momentum functions in the Heitler–London approach is then investigated (commonly called self‐consistent valence bond); the agreement with OPTX degrades, leading to a larger value of LRC and a smaller value of DC at H₂ equilibrium. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Electronic structure and spectroscopic properties of 6‐aminophenanthridine and its derivatives: Insights from density functional theory

6‐Aminophenanthridine (6AP) and its derivatives show important biological activities as antiprion compounds and inhibitors of the protein folding activity of the ribosome. Both of these activities depend on the RNA binding property of these compounds, which has been recently characterized by fluorescence spectroscopy. Hence, fundamental insights into the photophysical properties of 6AP compounds are highly important to understand their biological activities. In this work, we have calculated electronic structures and optical properties of 6AP and its three derivatives 6AP8CF₃, 6AP8Cl, and 6APi by density functional theory (DFT) and time‐dependent density functional theory (TDDFT). Our calculated spectra show a good agreement with the experimental absorption and fluorescence spectra, and thus, provide deep insights into the optical properties of the compounds. Furthermore, comparing the results obtained with four different hybrid functionals, we demonstrate that the accuracy of the functionals varies in the order B3LYP > PBE0 > M062X > M06HF. © 2015 Wiley Periodicals, Inc.     

Improved parameterization of the quantum harmonic oscillator model based on localized wannier functions to describe Van der Waals interactions in density functional theory

Recently, the quantum harmonic oscillator model has been combined with maximally localized Wannier functions to account for long‐range dispersion interactions in density functional theory calculations (Silvestrelli, J. Chem. Phys. 2013, 139, 054106). Here, we present a new, improved set of values for the three parameters involved in this scheme. To test the new parameter set we have computed the potential energy curves for various systems, including an isolated Ar2 dimer, two N2 dimers interacting within different configurations, and a water molecule physisorbed on pristine graphene. While the original set of parameters generally overestimates the interaction energies and underestimates the equilibrium distances, the new parameterization substantially improves the agreement with experimental and theoretical reference values. © 2016 Wiley Periodicals, Inc.