Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.     

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.     

Crystal structure and density functional theory study on structural properties and energies of a isonicotinohydrazide compound

An X-ray and a theoretical study of the structure of the isoniazid derivative N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate (1) are reported. In this work, we will report a combined experimental and theoretical study on the molecular structure, vibrational spectra and energies of N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate. The calculated parameters are in good agreement with the corresponding X-ray diffraction values. The FTIR spectrum in the range of 400-4000 cm-1 of N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate has been recorded. The molecular geometry and vibrational frequencies and energies in the ground state are calculated by using the DFT (B3LYP, PBE1PBE) methods with 6-311G** basis sets. The calculated HOMO and LUMO energies also confirm that charge transfer occurs within the molecule. The geometries and normal modes of vibrations obtained from B3LYP/PBE1PBE/6-311G** calculations are in good agreement with the experimentally observed data.     

Electronic structure and bonding of {Fe(PhNO2)}6 complexes: a density functional theory study

Reduction of nitro-aromatic compounds (NACs) proceeds through intermediates with a partial electron transfer into the nitro group from a reducing agent. To estimate the extent of such a transfer and, therefore, the activity of various model ferrous-containing reductants toward NAC degradation, the unrestricted density functional theory (DFT) in the basis of paired L?wdin-Amos-Hall orbitals has been applied to complexes of nitrobenzene (NB) and model Fe(II) hydroxides including cationic [FeOH]+, then neutral Fe(OH)2, and finally anionic [Fe(OH)3]-. Electron transfer is considered to be a process of unpairing electrons (without the change of total spin projection Sz) that reveals itself in a substantial spin contamination of the unrestricted solution. The unrestricted orbitals are transformed into localized paired orbitals to determine the orbital channels for a particular electron-transfer state and the weights of idealized charge-transfer and covalent electron structures. This approach allows insight into the electronic structure and bonding of the {Fe(PhNO2)}6 unit (according to Enemark and Feltham notation) to be gained using model nitrobenzene complexes. The electronic structure of this unit can be expressed in terms of pi-type covalent bonding [Fe+2(d6, S = 2) - PhNO2(S = 0)] or charge-transfer configuration [Fe+3(d5, S = 5/2) - {PhNO2}- ((pi*)1, S = 1/2)].     

Describing weak interactions of biomolecules with dispersion-corrected density functional theory

Interaction energies of the biomolecules in the JSCH-2005 database are calculated with density functional theory using the exchange-correlation functional BLYP augmented with dispersion-corrected atom-centered potentials (DCACPs). The results are in excellent agreement with extrapolated CCSD(T) complete basis set limit references with unsigned mean errors of less than 1.6 kcal mol(-1). Geometry optimisations all reach stable configurations that are close to the MP2-optimised reference geometries.     

Ring complexes of S-nitrosothiols with CU+: a density functional theory study

The density functional theory (DFT) method B3P86/6-311+G(2df,p) has been employed to investigate the complexes formed upon interaction of Cu(+) with nitrosylated cysteine (CysNO) and its decarboxylated (H(2)NCH(2)CH(2)SNO) and deaminated (HOOCCH(2)CH(2)SNO) derivatives. Optimized structures, relative enthalpies and relative free energies have been calculated and compared. In addition, the effects of binding an H(2)O molecule to the Cu(+) centre in the resulting complexes have also been considered. It is found that the most stable complexes are formed when Cu(+) coordinates to the S-nitrosothiol via S of the SNO group. This results in dramatic lengthenings of the SN bond with concomitant shortening of the NO bond. In contrast, when Cu(+) coordinates via the nitrogen of the SNO group, a shortening of the SN bond with lengthening of the NO bond is observed. These effects are tempered by the electron donating ability of other functional groups also coordinated with the Cu(+) centre in the complexes and on the coordination state of the Cu(+) ion.     

Fast prediction of hydration free energies for SAMPL4 blind test from a classical density functional theory

We report the performance of a classical density functional theory (CDFT) in the competition for the solvation free-energy category of the SAMPL4 blind prediction event. The theoretical calculations were carried out with the TIP3P water model and different combinations of solute configurations and molecular force fields. In comparison with the experimental data, the blind test yields an average unsigned error of 2.38 kcal/mol and the root mean square deviation of 2.99 kcal/mol. Whereas these numbers are significantly larger than the best results from explicit-solvent MD simulations, we find that the theoretical performance is sensitive to both the molecular force fields and solute configurations and that a comparable level of accuracy can be achieved by a judicious selection of the solute configurations and the force-field parameters. Most importantly, CDFT reduces the computational cost of MD simulation by almost 3 orders of magnitude, making it very attractive for large-scale hydration free-energy calculations (e.g., screening the aqueous solubility of drug-like molecules).     

Structure and ionization energies of some analogues of iron-only hydrogenases studied by density functional theory methods

Density functional theory calculations using both the B3LYP and BP86 functional in conjunction with a medium and large size basis set have been used to predict the structures and ionization energies of 12 models of iron-only hydrogenases. Although the structural predictions do not allow a clear discrimination between the different computational models, these models do yield significantly different adiabatic and vertical ionization energies. The closest agreement with experiment is given by the BP86 functional and the large all-electron basis. At this level of theory the adiabatic ionization energies are very close to experiment, but the vertical values are uniformly too small, leading to an underestimation of the reorganization energies. The calculations also suggest that measured ionization energies may help in identifying both the bridge-head group and whether CO bridging takes place upon ionization.     

The structure and binding energies of the van der Waals complexes of Ar and N2 with phenol and its cation, studied by high level ab initio and density functional theory calculations

We have investigated, using both ab initio and density functional theory methods, the minimum energy structures and corresponding binding energies of the van der Waals complexes between phenol and argon or the nitrogen molecule, and the corresponding complexes involving the phenol cation. Structures were obtained at the MP2 level using a large basis, and the corresponding energies were corrected for basis set superposition error (BSSE), higher order electron correlation effects, and for basis set size. The structures of the global minima were further refined for the effects of BSSE and the corresponding binding energies were evaluated. For each neutral species, we find only a single true minimum, pi bonded for argon and OH bonded for nitrogen. For both cationic species, we find that the OH-bonded complex is preferred over other minima which we have identified as having Ar or N(2) between exogeneous atoms. The ab initio calculations are generally in excellent agreement with experimental binding energies and rotational constants. We find that the B3LYP functional is particularly poor at describing these complexes, while a density functional theory (DFT) method with an empirical correction for dispersive interactions (DFT-D) is very successful, as are some of the new functionals proposed by Zhao and Truhlar [J. Phys. Chem. A 109, 5656 (2005); J. Chem. Theory Comput. 2, 1009 (2006); Phys. Chem. Chem. Phys. 7, 2701 (2005); J. Phys. Chem. A 108, 6908 (2004)]. Both the ab initio and DFT-D methods accurately predict the intermolecular vibrational modes.     

Communication: Density functional theory overcomes the failure of predicting intermolecular interaction energies

Density-functional theory (DFT) revolutionized the ability of computational quantum mechanics to describe properties of matter and is by far the most often used method. However, all the standard variants of DFT fail to predict intermolecular interaction energies. In recent years, a number of ways to go around this problem has been proposed. We show that some of these approaches can reproduce interaction energies with median errors of only about 5% in the complete range of intermolecular configurations. Such errors are comparable to typical uncertainties of wave-function-based methods in practical applications. Thus, these DFT methods are expected to find broad applications in modelling of condensed phases and of biomolecules.     

Nitrogen activation via three-coordinate molybdenum complexes: comparison of density functional theory performance with wave function based methods

Obtaining an accurate theoretical model for the activation of dinitrogen by three-coordinate molybdenum amide complexes (e.g. Mo(NH2)3) is difficult due to the interaction of various high- and low-spin open-shell complexes along the reaction coordinate which must be treated with comparable levels of accuracy in order to obtain reasonable potential energy surfaces. Density functional theory with present-day functionals is a popular choice in this situation; however, the dinitrogen activation reaction energetics vary substantially with the choice of functional. An assessment of the reaction using specialized wave function based methods indicates that although current density functionals in general agree qualitatively on the mechanistic details of the reaction, a variety of high-level electron correlation methods (including CCSD(T), OD(T), CCSD(2), KS-CCSD(T), and spin-flip CCSD) provide a consistent but slightly different representation of the system.     

Calculation of bond dissociation energies for oxygen containing molecules by ab initio and density functional theory methods

Two ab initio (ROHF and MP2), one local (SVWN), four hybrid (BHandH, BHandHLYP, Becke3LYP, and Becke3P86), and two nonlocal (BLYP and BP86) density functional theory (DFT) methods are used for calculating the dissociation energies of molecules that contain H(SINGLE BOND)O, O(SINGLE BOND)O and O(SINGLE BOND)C bonds. The sensitivity to the basis set of the prediction of bond dissociation energies with DFT methods was tested with Becke3LYP on the H(SINGLE BOND)O dissociation energy of water. The 6–31 + G(d) methods are chosen as the smallest basis set which produces reasonable results. The calculated values for all other ab initio and DFT methods were performed with these basis sets and then compared with the experimental data. The suitability of DFT methods for computing reliable bond dissociation energies of oxygen containing molecules is discussed. © 1996 John Wiley & Sons, Inc.     

Systematic study of the performance of density functional theory methods for prediction of energies and geometries of organoselenium compounds

A variety of density functional theory (DFT) methods are paired with Pople basis sets of varying sizes and evaluated for use with organoselenium compounds. The ability of each method to predict reliable geometries and energies is determined through comparison with quadratic configuration interaction with single and double excitations (QCISD) results. The recommended procedure for accurate prediction of energies and geometries is to use the B3PW91 functional with the 6-311G(2df,p) basis set. The B3PW91/6-31G(d,p) level of theory gives almost identical geometries as larger basis sets, so geometries can be predicted at this level for computational efficiency.     

Configuration interaction based on constrained density functional theory: a multireference method

Existing density functional theory (DFT) methods are typically very effective in capturing dynamic correlation, but run into difficulty treating near-degenerate systems where static correlation becomes important. In this work, we propose a configuration interaction (CI) method that allows one to use a multireference approach to treat static correlation but incorporates DFT's efficacy for the dynamic part as well. The new technique uses localized charge or spin states built by a constrained DFT approach to construct an active space in which the effective Hamiltonian matrix is built. These local configurations have significantly less static correlation compared to their delocalized counterparts and possess an essentially constant amount of self-interaction error. Thus their energies can be reliably calculated by DFT with existing functionals. Using a small number of local configurations as different references in the active space, a simple CI step is then able to recover the static correlation missing from the localized states. Practical issues of choosing configurations and adjusting constraint values are discussed, employing as examples the ground state dissociation curves of H(2) (+), H(2), and LiF. Excellent results are obtained for these curves at all interatomic distances, which is a strong indication that this method can be used to accurately describe bond breaking and forming processes.     

Linearity condition for orbital energies in density functional theory: construction of orbital-specific hybrid functional

This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: ?(2)E/?f(i)(2)|(0≤f(i)≤1) = ??(i)/?f(i)|(0≤f(i)≤1) = 0, where E, ε(i), and f(i) represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree-Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans' theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core-valence-Rydberg-Becke-3-parameter-Lee-Yang-Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)].     

Benchmark of density functional theory methods on the prediction of bond energies and bond distances of noble-gas containing molecules

We have tested three pure density functional theory (DFT) functionals, BLYP, MPWPW91, MPWB95, and ten hybrid DFT functionals, B3LYP, B3P86, B98, MPW1B95, MPW1PW91, BMK, M05-2X, M06-2X, B2GP-PLYP, and DSD-BLYP with a series of commonly used basis sets on the performance of predicting the bond energies and bond distances of 31 small neutral noble-gas containing molecules. The reference structures were obtained using the CCSD(T)∕aug-cc-pVTZ theory and the reference energies were based on the calculation at the CCSD(T)∕CBS level. While in general the hybrid functionals performed significantly better than the pure functionals, our tests showed a range of performance by these hybrid functionals. For the bond energies, the MPW1B95∕6-311+G(2df,2pd), BMK∕aug-cc-pVTZ, B2GP-PLYP∕aug-cc-pVTZ, and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 2.0-2.3 kcal∕mol per molecule. For the bond distances, the MPW1B95∕6-311+G(2df,2pd), MPW1PW91∕6-311+G(2df,2pd), and B3P86∕6-311+G(2df,2pd), DSD-BLYP∕6-311+G(2df,2pd), and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 0.008-0.013 A? per bond. The current study showed that a careful selection of DFT functionals is very important in the study of noble-gas chemistry, and the most recommended methods are MPW1B95∕6-311+G(2df,2pd) and DSD-BLYP∕aug-cc-pVTZ.