Hydrogen-bonding interactions in acetonitrile oligomers using density functional theory method

Hydrogen-bonding interaction in acetonitrile oligomers is studied using density functional theory method. Two types of hydrogen-bonded oligomers are considered viz. cyclic and ladder. Different levels are used to optimize the geometry of acetonitrile monomer and found that at B3LYP/aug-cc-pvtz level the geometrical parameters and vibrational frequencies are in agreement with the experimental determinations. The BSSE corrected total energies of acetonitrile oligomers show that the cyclic structures are more stable than the ladder and the hydrogen bonds in former are stronger than those in the latter. Many-body analysis approach was used to study the nature of interactions between different molecules in these oligomers. It is found that the contribution from many-body energies to the binding energy of a complex is different in cyclic and ladder structures. An increase and decrease in the energy per hydrogen bond with cluster size for the cyclic and ladder structures, respectively, indicates the positive and negative hydrogen-bond cooperativity, respectively.     

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.     

Performance of dispersion-corrected density functional theory for the interactions in ionic liquids

Potential energy curves for the dissociation of cation-anion associates representing the building units of ionic liquids have been computed with dispersion corrected DFT methods. Non-local van der Waals density functionals (DFT-NL) for the first time as well as an atom pair-wise correction method (DFT-D3) have been tested. Reference data have been computed at the extrapolated MP2/CBS and estimated CCSD(T)/CBS levels of theory. The investigated systems are combined from two cations (1-butyl-3-methylimidazolium and tributyl(methyl)posphonium) and three anions (chloride, dicyanamide, acetate). We find substantial stabilization from London dispersion energy near equilibrium of 5-7 kcal mol(-1) (about 5-6% of the interaction energy). Equilibrium distances are shortened by 0.03-0.09 ? and fundamental (inter-fragment) vibrational frequencies (which are in the range 140-180 cm(-1)) are increased by typically 10 cm(-1) when dispersion corrections are made. The dispersion-corrected hybrid functional potentials are in general in excellent agreement with the corresponding CCSD(T) reference data (typical deviations of about 1-2%). The DFT-D3 method performs unexpectedly well presumably because of cancellation of errors between the dispersion coefficients of the cations and anions. Due to self-interaction error, semi-local density functionals exhibit severe SCF convergence problems, and provide artificial charge-transfer and inaccurate interaction energies for larger inter-fragment distances. Although these problems may be alleviated in condensed phase simulations by effective Coulomb screening, only dispersion-corrected hybrid functionals with larger amounts of Fock-exchange can in general be recommended for such ionic systems.     

Interatomic interactions in momentum space. Momentum density and kinetic energy in chemical bonding

On the basis of the virial theorem for a uniform scaling process of a polyatomic system, the total energy and its gradient are quantitatively related with the behavior of the electron density in momentum space through the kinetic energy of the system. For attractive and repulsive interactions, the behavior of the momentum density distribution and its effect on the stabilization energy and the interatomic force are examined. Some guiding principles are deduced for their interrelation. The results are used to clarify the role of kinetic energy in chemical bonding. Possible energy partitioning in this approach is also mentioned.     

A density functional theory approach to noncovalent interactions via interacting monomer densities

A recently proposed "DFT + dispersion" treatment (Rajchel et al., Phys. Rev. Lett., 2010, 104, 163001) is described in detail and illustrated by more examples. The formalism derives the dispersion-free density functional theory (DFT) interaction energy and combines it with the dispersion energy from separate DFT calculations. It consists of the self-consistent polarization of DFT monomers restrained by the exclusion principle via the Pauli blockade technique. Within the monomers a complete exchange-correlation potential should be used, but between them only the exact exchange operates. The application to a wide range of molecular complexes from rare-gas dimers to hydrogen-bonds to π-electron interactions shows good agreement with benchmark values.     

Critical examination of the supermolecule density functional theory calculations of intermolecular interactions

The results of calculations employing twelve different combinations of exchange and correlation functionals are compared with results of ab initio calculations for two different configurations of the water dimer and three different configurations of the thymine-adenine complex. None of the density functional theory (DFT) treatments could properly reproduce the results of coupled-cluster calculations for all configurations examined. The DFT approaches perform well when the interaction energy is dominated by the electrostatic component and the dispersion energy is less important. Two mechanisms that compensate for the missing dispersion component were identified. The first one is the decrease of the magnitude of the intermolecular exchange-repulsion and the second one is the increase of the magnitude of the attractive deformation energy. For some functionals both effects are observed together, but for some other ones only the second effect occurs. The three correlation functionals that were examined were found to make only very small contributions to the deformation energy. The examination of angular and distance dependence of the interactions shows that the currently available DFT approaches are not suitable for developing intermolecular potential energy surfaces. They could however be used to find global minima on potential energy surfaces governed by intermolecular electrostatic interactions. Additional single point ab initio calculations are recommended as the means of validating optimized structures.     

Embedding wave function theory in density functional theory

We present a framework for embedding a highly accurate coupled-cluster calculation within a larger density functional calculation. We use a perturbative buffer to help insulate the coupled-cluster region from the rest of the system. Regions are defined, not in real space, but in Hilbert space, though connection between the two can be made by spatial localization of single-particle orbitals. Relations between our embedding approach and some similar techniques are discussed. We present results for small sample systems for which we can extract essentially exact results, demonstrating that our approach seems to work quite well and is generally more reliable than some of the related approaches due to the introduction of additional interaction terms.     

Molecular fragments in density functional theory

The second-order density functional approach to the partitioning of the molecular density of Cedillo, Chattaraj, and Parr (Int. J. Quantum Chem. 2000, 77, 403-407) is used, together with a local assumption for the function that projects the total density into its components, to show that the distribution function adopts a stockholders form, in terms of the local softness of the isolated fragments, and that the molecular Fukui function is distributed in the molecular fragments in the same proportion as the electronic density.     

Multigrid methods in density functional theory

A multigrid method for real-space solution of the Kohr-Sham equations is presented. By using this multiscale approach, the problem of critical slowing down typical of iterative real-space solvers is overcome. The method scales linearly in computer time with the number of electrons if the orbitals are localized. Here, we describe details of our multigrid method, present preliminary many-electron numerical results illustrating the efficiency of the solver, and discuss its strengths and limitations. © 1997 John Wiley & Sons, Inc.     

Pseudospectral time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is implemented within the Tamm-Dancoff approximation (TDA) using a pseudospectral approach to evaluate two-electron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunction-based methods with similar conclusions. The pseudospectral TDA-TDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.     

Orbital-corrected orbital-free density functional theory

A new implementation of density functional theory (DFT), namely orbital-corrected orbital-free (OO) DFT, has been developed. With at most two non-self-consistent iterations, OO-DFT accomplishes the accuracy comparable to fully self-consistent Kohn-Sham DFT as demonstrated by its application on the cubic-diamond Si and the face-centered-cubic Ag systems. Our work provides a new impetus to further improve orbital-free DFT method and presents a robust means to significantly lower the cost associated with general applications of linear-scaling Kohn-Sham DFT methods on large systems of thousands of atoms within different chemical bonding environment.     

Perspective on density functional theory

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science. Electronic structure problems in a dazzling variety of fields are currently being tackled. However, DFT has many limitations in its present form: too many approximations, failures for strongly correlated systems, too slow for liquids, etc. This perspective reviews some recent progress and ongoing challenges.     

Interatomic versus intraatomic Ru interactions in perovskites

The competition between interatomic Ru-O-Ru interactions responsible for itinerant-electron ferromagnetism in SrRuO₃ and intraatomic spin-orbit coupling that suppresses some Ru-O-Ru magnetic interactions in CaRuO₃ so as to prevent long-range magnetic order has been further tested by investigating the double perovskites La₂RuZnO₆, La₂RuCoO₆, La₂TiCoO₆, and the solid solution Ca_2−2xLa_2xRu_2−xCo_xO₆ (0.0?x?1.0). The paramagnetic state of the low-spin, localized Ru⁴⁺:t⁴e⁰ configuration of LaRuZnO₆ undergoes a progressive transition on lowering the temperature to a non-magnetic state (J=0) as a result of spin-orbit coupling, λL·S. Comparison of the susceptibilities of La₂RuCoO₆ and La₂TiCoO₆ shows a similar behavior with long-range antiferromagnetic cobalt ordering via non-magnetic RuO_6/2 and TiO_6/2 bridges. Comparison is also made of the effect of substituting Ga for Ru in CaRuO₃ with the effect of other dopants M in CaRu_1−xM_xO₃. The evolution of transport properties in Ca_2−2xLa_2xRu_2−xCo_xO₆ is also presented.     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Noncovalent interactions in paired DNA nucleobases investigated by terahertz spectroscopy and solid-state density functional theory

Cocrystallized adenine and thymine derivatives, along with the pure monomeric crystals, were investigated by terahertz spectroscopy and solid-state density functional theory (DFT). The methylated nucleobase derivatives crystallize in planar hydrogen-bonded adenine-thymine pairs similar to the manner found in DNA. The spectra obtained for 1-methylthymine, 9-methyladenine, and the 1:1 cocrystal in the range of 10-100 cm(-1) clearly demonstrate that absorptions in this spectral range originate from the uniquely ordered assembly and the intermolecular interactions found in each individual crystal system. The quality of spectral reproduction for the DFT simulations of each system was clearly improved by the inclusion of an empirical correction term for London-type dispersion forces to the calculations. Notably, it was found that these weak dispersion forces in the adenine-thymine cocrystal were necessary to produce a properly converged crystal structure and meaningful simulation of the terahertz vibrational spectrum.     

Carbohydrate-protein recognition probed by density functional theory and ab initio calculations including dispersive interactions

Carbohydrate-protein recognition has been studied by electronic structure calculations of complexes of fucose and glucose with toluene, p-hydroxytoluene and 3-methylindole, the latter aromatic molecules being analogues of phenylalanine, tyrosine and tryptophan, respectively. We use mainly a density functional theory model with empirical corrections for the dispersion interactions (DFT-D), this method being validated by comparison with a limited number of high level ab initio calculations. We have calculated both binding energies of the complexes as well as their harmonic vibrational frequencies and proton NMR chemical shifts. We find a range of minimum energy structures in which the aromatic group can bind to either of the two faces of the carbohydrate, the binding being dominated by a combination of OH-pi and CH-pi dispersive interactions. For the fucose-toluene and alpha-methyl glucose-toluene complexes, the most stable structures involve OH-pi interactions, which are reflected in a red shift of the corresponding O-H stretching frequency, in good quantitative agreement with experimental data. For those structures where CH-pi interactions are found we predict a corresponding blue shift in the C-H frequency, which parallels the predicted proton NMR shift. We find that the interactions involving 3-methylindole are somewhat greater than those for toluene and p-hydroxytoluene.