Density functionals for noncovalent interaction energies of biological importance (original) (raw)
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Blind test of density-functional-based methods on intermolecular interaction energies
The Journal of Chemical Physics, 2016
In the past decade, a number of approaches have been developed to fix the failure of (semi)local density-functional theory (DFT) in describing intermolecular interactions. The performance of several such approaches with respect to highly accurate benchmarks is compared here on a set of separation-dependent interaction energies for ten dimers. Since the benchmarks were unknown before the DFT-based results were collected, this comparison constitutes a blind test of these methods. [
The Journal of Physical Chemistry A, 2007
Recently, two computational approaches that supply a density-functional-based quantum-chemical method with an empirical term accounting for London dispersion were introduced and found use in the studies of biomolecular systems, namely, DFT-D and SCC-DFTB-D. Here, we examine the performance and usability of these combined techniques for dealing with several tasks typically occurring in the research of biomolecules. The interaction energy of small biomolecular complexes agrees very well with the reference data yielded by correlated ab initio quantum chemical methods. In real-life studies aimed at interaction energy, structure, and infrared spectra, the mentioned methods provide results in good agreement with each other and with experiment (where available). The very favorable time demands of these approaches are discussed, and for each of them, a suitable area of use is proposed on the basis of the results of our analysis.
Journal of Computational Chemistry, 2007
Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high-level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated-B-LYP, B3-LYP, PBE, TPSS, TPSSh, and BH-LYPand even surpass the MP2/cc-pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, s R , scaling globally the vdW radii. For good results, a basis set of at least triple-quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen-bonded and stacked complexes considered, respectively.
Journal of Molecular Modeling, 2007
Interaction energies for a representative sample of 39 intermolecular complexes are calculated using two computational approaches based on the subsystem formulation of density functional theory introduced by Cortona (Phys. Rev. B 44:8454, 1991), adopted for studies of intermolecular complexes (Wesolowski and Weber in Chem. Phys. Lett. 248:71, 1996). The energy components (exchange-correlation and non-additive kinetic) expressed as explicit density functionals are approximated by means of gradient-free-(local density approximation) of gradientdependent-(generalized gradient approximation) approximations. The sample of the considered intermolecular complexes was used previously by Zhao and Truhlar to compare the interaction energies derived using various methods based on the Kohn-Sham equations with highlevel quantum chemistry results considered as the reference. It stretches from rare gas dimers up to strong hydrogen bonds. Our results indicate that the subsystem-based methods provide an interesting alternative to that based on the Kohn-Sham equations. Local density approximation, which is the simplest approximation for the relevant density functionals and which does not rely on any empirical data, leads to a computational approach comparing favorably with more than twenty methods based on the Kohn-Sham equations including the ones, which use extensively empirical parameterizations. For various types of nonbonding interactions, the strengths and weaknesses of gradient-free and gradient-dependent approximations to exchange-correlation and non-additive kinetic energy density functionals are discussed in detail.
The Journal of Chemical Physics, 2009
This paper presents an approach for obtaining accurate interaction energies at the DFT level for systems where dispersion interactions are important. This approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)] method for the evaluation of dispersion energy corrections and a Hirshfeld method for partitioning of molecular polarizability tensors into atomic contributions. Due to the availability of atomic polarizability tensors, the method is extended to incorporate anisotropic contributions, which prove to be important for complexes of lower symmetry. The method is validated for a set of eighteen complexes, for which interaction energies were obtained with the B3LYP, PBE and TPSS functionals combined with the aug-cc-pVTZ basis set and compared with the values obtained at CCSD(T) level extrapolated to a complete basis set limit. It is shown that very good quality interaction energies can be obtained by the proposed method for each of the examined functionals, the overall performance of the TPSS functional being the best, which with a slope of 1.00 in the linear regression equation and a constant term of only 0.1 kcal/mol allows to obtain accurate interaction energies without any need of a damping function for complexes close to their exact equilibrium geometry.
Journal of Chemical Theory and Computation, 2007
The reliable prediction of molecular properties is a vital task of computational chemistry. In recent years, density functional theory (DFT) has become a popular method for calculating molecular properties for a vast array of systems varying in size from small organic molecules to large biological compounds such as proteins. In this work we assess the ability of many DFT methods to accurately determine atomic and molecular properties for small molecules containing elements commonly found in proteins, DNA, and RNA. These properties include bond lengths, bond angles, ground state vibrational frequencies, electron affinities, ionization potentials, heats of formation, hydrogen bond interaction energies, conformational energies, and reaction barrier heights. Calculations are carried out with the 3-21G*, 6-31G*, 3-21+G*, 6-31+G*, 6-31++G*, cc-pVxZ, and aug-cc-pVxZ (x=D,T) basis sets, while bond distance and bond angle calculations are also done using the cc-pVQZ and aug-cc-pVQZ basis sets. Members of the popular functional classes, namely, LSDA, GGA, meta-GGA, hybrid-GGA, and hybrid-meta-GGA, are considered in this work. For the purpose of comparison, Hartree-Fock (HF) and second order many-body perturbation (MP2) methods are also assessed in terms of their ability to determine these physical properties. Ultimately, it is observed that the split valence bases of the 6-31G variety provide accuracies similar to those of the more computationally expensive Dunning type basis sets. Another conclusion from this survey is that the hybrid-meta-GGA functionals are typically among the most accurate functionals for all of the properties examined in this work.
Improving Results by Improving Densities: Density-Corrected Density Functional Theory
Journal of the American Chemical Society
DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This article explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.
Benchmark databases for nonbonded interactions and their use to test density functional theory
Journal of Chemical Theory and …, 2005
We present four benchmark databases of binding energies for nonbonded complexes. Four types of nonbonded interactions are considered: hydrogen bonding, charge transfer, dipole interactions, and weak interactions. We tested 44 DFT methods and 1 WFT method against the new databases; one of the DFT methods (PBE1KCIS) is new, and all of the other methods are from the literature. Among the tested methods, the PBE, PBE1PBE, B3P86, MPW1K, B97-1, and BHandHLYP functionals give the best performance for hydrogen bonding. MPWB1K, MP2, MPW1B95, MPW1K, and BHandHLYP give the best performances for charge transfer interactions; and MPW3LYP, B97-1, PBE1KCIS, B98, and PBE1PBE give the best performance for dipole interactions. Finally, MP2, B97-1, MPWB1K, PBE1KCIS, and MPW1B95 give the best performance for weak interactions. Overall, MPWB1K is the best of all the tested DFT methods, with a relative error (highly averaged) of only 11%, and MPW1K, PBE1PBE, and B98 are the best of the tested DFT methods that do not contain kinetic energy density. Moving up the rungs of Jacob's ladder for nonempirical DFT, PBE improves significantly over the LSDA, and TPSS improve slightly over PBE (on average) for nonbonded interactions. 6 theory for several more nonbonded complexes in the present work. The strengths and limitations of W1 theory have been described elsewhere. 98,105,108,109,119 2.2. HB6/04 Database. The hydrogen bond database consists of binding energies of six hydrogen bonding dimers, namely (NH 3 ) 2 , (HF) 2 , (H 2 O) 2 , NH 3 ···H 2 O, (HCONH 2 ) 2 , and (HCOOH) 2 . The binding energies of (NH 3 ) 2 , (HF) 2 , (H 2 O) 2 , and NH 3 ···H 2 O are taken from Boese and Martin's 81 W2 calculations. The best estimates of D e for (HCONH 2 ) 2 and (HCOOH) 2 are calculated here by the W1 theory. This database is called the HB6/04 database. 2.3. CT7/04 Database. The charge transfer (CT) database consists of binding energies of seven charge transfer complexes, in particular C 2 H 4 ···F 2 , NH 3 ···F 2 , C 2 H 2 ···ClF, HCN···ClF, NH 3 ···Cl 2 , H 2 O···ClF, and NH 3 ···ClF. The best estimates of D e for all complexes in the charge transfer database are calculated here by the W1 model. This database is called the CT7/04 database. 2.4. DI6/04 Database. The dipole interaction (DI) database consists of binding energies of six dipole inteaction complexes: (H 2 S) 2 , (HCl) 2 , HCl···H 2 S, CH 3 Cl···HCl, CH 3 SH···HCN, and CH 3 SH···HCl. The binding energy of (HCl) 2 is taken from Boese and Martin's 81 W2 calculation. The best estimates of D e for the other complexes in the dipole interaction database are calculated here by the W1 theory. This database is called the DI6/04 database. 2.5. WI9/04 Database. The weak interaction database consists of binding energies of weak interaction complexes, namely HeNe, HeAr, Ne 2 , NeAr, CH 4 ···Ne, C 6 H 6 ···Ne, (CH 4 ) 2 , (C 2 H 2 ) 2 , and (C 2 H 4 ) 2 . The binding energies of HeNe, HeAr, Ne 2 , and NeAr are taken from Ogilvie and Wang's 130,131 analysis. The binding energy of C 6 H 6 ···Ne is taken from Capplelleti et al.'s 132 experimental study. The best estimates of D e for CH 4 ···Ne, (CH 4 ) 2 , (C 2 H 2 ) 2 , and (C 2 H 4 ) 2 are calculated by W1 theory. This database is called the WI9/04 database.