Adiabatic corrections to density functional theory energies and wave functions

The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT.     

An improved theoretical approach to the empirical corrections of density functional theory

An empirical correction to density functional theory (DFT) has been developed in this study. The approach, called correlation corrected atomization–dispersion (CCAZD), involves short- and long-range terms. Short-range correction consists of bond (1,2-) and angle (1,3-) interactions, which remedies the deficiency of DFT in describing the proto-branching stabilization effects. Long-range correction includes a Buckingham potential function aiming to account for the dispersion interactions. The empirical corrections of DFT were parameterized to reproduce reported ΔH _f values of the training set containing alkane, alcohol and ether molecules. The ΔH _f of the training set molecules predicted by the CCAZD method combined with two different DFT methods, B3LYP and MPWB1K, with a 6-31G* basis set agreed well with the experimental data. For 106 alkane, alcohol and ether compounds, the average absolute deviations (AADs) in ΔH _f were 0.45 and 0.51 kcal/mol for B3LYP- and MPWB1K-CCAZD, respectively. Calculations of isomerization energies, rotational barriers and conformational energies further validated the CCAZD approach. The isomerization energies improved significantly with the CCAZD treatment. The AADs for 22 energies of isomerization reactions were decreased from 3.55 and 2.44 to 0.55 and 0.82 kcal/mol for B3LYP and MPWB1K, respectively. This study also provided predictions of MM4, G3, CBS-QB3 and B2PLYP-D for comparison. The final test of the CCAZD approach on the calculation of the cellobiose analog potential surface also showed promising results. This study demonstrated that DFT calculations with CCAZD empirical corrections achieved very good agreement with reported values for various chemical reactions with a small basis set as 6-31G*.     

Time-dependent density functional theory calculations of the photoabsorption of fluorinated alkanes

Time-dependent density functional theory (TD-DFT) calculations of the transition energies and oscillator strengths of fluorinated alkanes have been performed. The TD-DFT method with the non-local B3LYP potential yields transition energies for the methanes, which are smaller by about 10% as compared to the experimental values. An empirical linear correlation was found between the calculated and experimental transition energies both at the B3LYP/DZ+Ryd(C, F) and B3LYP/cc-pVTZ+Ryd(C, F, H) levels for a total of 19 transitions of the fluorinated methanes with linear correlation coefficients of 0.987 for the former and 0.988 for the latter. This empirical correlation for fluorinated methane molecules is found to agree well with the previously obtained empirical correlations between calculated and experimental values for non-fluorinated molecules. The results show that a single empirical-correlation relationship can be used for both non-fluorinated and fluorinated molecules to predict transition energies. This linear relationship is then used to predict the photoabsorption spectra of ethane, propane, butane, and partially and fully fluorinated derivatives. A key result of these calculations is the dominance of Rydberg transitions in the spectral region of interest.     

Influence of nonbonded intramolecular interactions on the vibrational frequencies of molecules

The nature of the displacement of the frequency of a characteristic vibration under the influence of the nonbonded interactions of atoms within a molecule (the field effect) has been studied. It has been shown in the example of the interaction of the bonds in the tetratomic Cl-C-C=O fragment that the (C=O) frequency increases under the influence of the dipole-dipole interaction of the C=O and C-Cl bonds; the same interaction causes a decrease in the freqency, if the Cl atom is replaced by an electropositive atom. The physical meaning which should be imparted to the Urey-Bradley potential, in particular, follows from the analysis presented.Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 24, No. 1, pp. 100–104, January–February, 1988.     

Performance of density functional theory methods to describe intramolecular hydrogen shifts

The performance of three exchange and correlation density functionals, LDA, BLYP and B3LYP, with four basis sets is tested in three intramolecular hydrogen shift reactions. The best reaction and activation energies come from the hybrid functional B3LYP with triple-ζ basis sets, when they are compared with high-level post-Hartree-Fock results from the literature. For a fixed molecular geometry, the electrophilic Fukui function is computed from a finite difference approximation. Fukui function shows a small dependence with both the exchange and correlation functional and the basis set. Evolution of the Fukui function along the reaction path describes important changes in the basic sites of the corresponding molecules. These results are in agreement with the chemical behavior of those species.     

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.     

Application of semiempirical long-range dispersion corrections to periodic systems in density functional theory

Ewald summation is used to apply semiempirical long-range dispersion corrections (Grimme, J Comput Chem 2006, 27, 1787; 2004, 25, 1463) to periodic systems in density functional theory. Using the parameters determined before for molecules and the Perdew-Burke-Ernzerhof functional, structure parameters and binding energies for solid methane, graphite, and vanadium pentoxide are determined in close agreement with observed values. For methane, a lattice constant a of 580 pm and a sublimation energy of 11 kJ mol(-1) are calculated. For the layered solids graphite and vanadia, the interlayer distances are 320 pm and 450 pm, respectively, whereas the graphite interlayer energy is -5.5 kJ mol(-1) per carbon atom and layer. Only when adding the semiempirical dispersion corrections, realistic values are obtained for the energies of adsorption of C(4) alkenes in microporous silica (-66 to -73 kJ mol(-1)) and the adsorption and chemisorption (alkoxide formation) of isobutene on acidic sites in the micropores of zeolite ferrierite (-78 to -94 kJ mol(-1)). As expected, errors due to missing self-interaction correction as in the energy for the proton transfer from the acidic site to the alkene forming a carbenium ion are not affected by the dispersion term. The adsorption and reaction energies are compared with the results from M?ller-Plesset second-order perturbation theory with basis set extrapolation.     

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.     

Potentials in density functional theory and the importance of sum rules

In an ab initio approach to density functional theory one needs to know the electronic pair-density averaged over the coupling strength of the pair-interaction. As this pair-function is not available without having solved the associated N-electron problem, one has to resort to universal properties of the pair-density that are independent of specific features of the ground-state wavefunction. By exploiting these universal properties and so-called sum rules for the pair-correlation factors we derive very simple approximate spin-dependent expressions for the exchange-correlation energy per particle and for the associated potential in the Kohn-Sham equations. There is some similarity of the resulting density functionals with those obtained from the widely applied local spin density approximation (LSDA) based on electron gas theory. As the application of the latter to exceedingly inhomogeneous gases in realistic systems is very debatable, the manifest similarity seems to suggest that LSDA can consistently be justified only via the above pair-density analysis, but the justification of certain electron gas refinements may remain questionable. We shortly review similar attempts made by other authors and particularly focus on the issue of self-interaction and the “overbinding problem”. We demonstrate for the 3d- and 4d-metals that our approximation yields density of states (DOS), magnetic moments and Stoner parameters that are practically identical with respective data obtained from up-to-date LSDA- or gradient corrected (GGA-)potentials. There is also an excellent agreement of the DOS for the insulators (semi-conductors) C, Si, Ge, and GaAs. We show that our approach yields cohesive energies for these materials that are very close to the GGA-values indicating a distinct improvement over the standard LSDA-values. The calculations have been performed with the aid of the WIEN 97 computer code based on the Full Potential Linear Augmented Plane Wave (FLAPW-) method.     

Gradient corrections in the energy density functional

It is shown, by calculations in He and Ne with HF densities, that the improvement obtained when gradient corrections are added to the local approximation to the kinetic energy, arises from a detailed improvement in the kinetic energy density.     

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.     

A perturbation density functional theory for the competition between inter and intramolecular association

Using the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient.     

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.     

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.     

Additive density functional correlation corrections to single particle theories

The correlation energy functional E_c of the Hartree-Fock density is investigated. It was previously established that E_c produces the exact ground-state energy when added to the Hartree-Fock energy. Except when certain degeneracies occur, it is here shown that E_c is bounded from below when the coordinates of the Hartree-Fock density are scaled uniformly by λ, as λ → ∞. Consequently, approximations to E_c should display this bounded property, which is a second-order perturbation energy. It is also shown that a corresponding result applies to that correlation energy functional, Ë_c, which is to be added to a completed exact exchange-only (in the OPM sense) density functional calculation. Scaling requirements are presented for each order in the perturbation expansion for Ë_c. For instance, the second-order term is dimensionless. © 1997 John Wiley & Sons, Inc.     

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.