A perturbation theory without energy corrections

We employ logarithmic perturbation theory in a form that utilizes the force, instead of the potential, and yields equations for wavefunction‐correction terms without requiring any information of energy corrections at any stage. The knowledge of unperturbed eigenfunctions of other states is also unnecessary. The perturbed energy eigenvalue can be obtained as a series either by going back to the parent equation, or as an average value involving the perturbed state. The latter scheme applies to any other average property as well. Both ground and excited states of a few systems are chosen for demonstrative calculations. Influence of the nodal structure on the exponential function controlling spatial behavior of the probability density is discussed. Interrelations among specific correction terms are shown in the small‐ and large‐x regime; in the latter case, certain terms nicely sum up to yield the correct decay characteristics of the probability density as well. Relevance of the basic equation to an alternative, nonperturbative scheme of approximation is also outlined. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Isomers of C24. Density functional studies including gradient corrections

Density functional techniques are used to investigate the relative energies of seven different structural isomers of C₂₄. The traditional local density approximation yields the fullerene-like isomer to be the most stable. As in the case of C₂₀, the inclusion of gradient corrections has a dramatic effect on the relative energies. The gradient-corrected B-LYP method yields the monocyclic ring and graphite-like isomers to be almost isoenergetic (and most stable) while the bicyclic ring, fullerene-like, and bowl-like isomers are progressively higher in energy. The Hartree—Fock results are quite similar to the B-LYP results. Implications to fullerene growth mechanisms are pointed out.     

Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.     

The effects of nonlocal gradient corrections in density functional calculations of hydrocarbon radical hyperfine structures

Ground-state equilibrium geometries and hyperfine structures of a number of organic neutral and charged radical compounds are computed using the linear combination of Gaussian-type orbitals–density functional theory method. In addition to the local spin-density approximation, we also use two different nonlocal (gradient corrected) schemes for the calculations of the exchange and correlation potentials. The different functional forms are found to generate slightly different total and unpaired spin-density distributions in the molecules, and as a result, the computed isotropic hyperfine coupling constants vary markedly. The smallest variations are found for the hydrogens, where the results are generally in satisfactory agreement with experiment. For the carbon atoms, however, large differences in isotropic coupling constants are observed. The anisotropic hyperfine structures are generally very well described at all levels of theory. © John Wiley & Sons, Inc.     

Importance of the correlation contribution for local hybrid functionals: range separation and self-interaction corrections

Local hybrid functionals with their position-dependent exact-exchange admixture are a conceptually simple and promising extension of the concept of a hybrid functional. Local hybrids based on a simple mixing of the local spin density approximation (LSDA) with exact exchange have been shown to be successful for thermochemistry, reaction barriers, and a range of other properties. So far, the combination of this generation of local hybrids with an LSDA correlation functional has been found to give the most favorable results for atomization energies, for a range of local mixing functions (LMFs) governing the exact-exchange admixture. Here, we show that the choice of correlation functional to be used with local hybrid exchange crucially influences the parameterization also of the exchange part as well as the overall performance. A novel ansatz for the correlation part of local hybrids is suggested based on (i) range-separation of LSDA correlation into short-range (SR) and long-range (LR) parts, and (ii) partial or full elimination of the one-electron self-correlation from the SR part. It is shown that such modified correlation functionals allow overall larger exact exchange admixture in thermochemically competitive local hybrids than before. This results in improvements for reaction barriers and for other properties crucially influenced by self-interaction errors, as demonstrated by a number of examples. Based on the range-separation approach, a fresh view on the breakdown of the correlation energy into dynamical and non-dynamical parts is suggested.     

A β-lactam-azasugar hybrid as a competitive potent galactosidase inhibitor

A β-lactam-azasugar hybrid (polyhydroxylated carbacephem) has been designed and synthesized as a potent glycosidase inhibitor.     

Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections

We propose a long-range corrected hybrid meta-generalized-gradient approximation (GGA) functional, based on a global hybrid meta-GGA functional, M05 [Y. Zhao, N. E. Schultz, and D. G. Truhlar, J. Chem. Phys. 123, 161103 (2005)], and empirical atom-atom dispersion corrections. Our resulting functional, ωM05-D, is shown to be accurate for a very wide range of applications, such as thermochemistry, kinetics, noncovalent interactions, equilibrium geometries, frontier orbital energies, fundamental gaps, and excitation energies. In addition, we present three new databases, IP131 (131 ionization potentials), EA115 (115 electron affinities), and FG115 (115 fundamental gaps), consisting of experimental molecular geometries and accurate reference values, which will be useful in the assessment of the accuracy of density functional approximations.     

First-order relativistic corrections to MP2 energy from standard gradient codes: Comparison with results from density functional theory

The evaluation of the first-order scalar relativistic corrections to MP2 energy based on either direct perturbation theory or the mass–velocity and Darwin terms is discussed. In a basis set of Lévy-Leblond spinors the one- and two-electron matrix elements of the relativistic Hamiltonian can be decomposed into a nonrelativistic part and a relativistic perturbation. Thus, a program capable of calculating nonrelativistic energy gradients can be used to calculate the cross-term between relativity and correlation. The method has been applied to selected closed-shell atoms (He, Be, Ne, and Ar) and molecules (CuH, AgH, and AuH). The calculated equilibrium distances and harmonic frequencies were compared with results from first-order relativistic density functional calculations. It was found that the cross-term is not the origin of the nonadditivity of relativistic and correlation effects. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1596–1603, 1998     

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.     

Evaluation of a combination of local hybrid functionals with DFT-D3 corrections for the calculation of thermochemical and kinetic data

Due to their position-dependent exact exchange admixture, local hybrid functionals offer a higher flexibility and thus the potential for more universal and accurate exchange correlation functionals compared to global hybrids with a constant admixture, as has been demonstrated in previous work. Yet, the local hybrid constructions used so far do not account for the inclusion of dispersion-type interactions. As a first exploratory step toward a more general approach that includes van der Waals-type interactions with local hybrids, the present work has added DFT-D3-type corrections to a number of simple local hybrid functionals. Optimization of only the s(8) and s(r,6) parameters for the S22 set provides good results for weak interaction energies but deteriorates the excellent performance of the local hybrids for G3 atomization energies and for classical reaction barriers. A combined optimization of the two DFT-D3 parameters with one of the two parameters of the spin-polarized local mixing function (LMF) of a local hybrid for a more general optimization set provides simultaneously accurate dispersion energies, improved atomization energies, and accurate reaction barriers, as well as excellent alkane protobranching ratios. For other LMFs, the improvements of such a combined optimization for the S22 energies have been less satisfactory. The most notable advantage of the dispersion-corrected local hybrids over, for example, a B3LYP-D3 approach, is in the much more accurate reaction barriers.     

Investigations of hydrogen-bonded systems: Local density approximation and gradient corrections

The applicability of the local density approximation (LDA ) and of corresponding gradient corrections (for the exchange and correlation energy) for the treatment of the hydrogen bond is investigated. As test systems, we consider the water dimer and the H₂O…?HX complexes (X = F, Cl, Br): Using an LCAO scheme, their equilibrium geometries and interaction energies are ?alculated and compared with experimental data and with other calculations. We obtain that the LDA gives the geometries in qualitative agreement with other data, whereas the energies are overestimated. The use of the gradient corrections (GC ) according to Becke and Perdew leads to a significant improvement of the geometry, and especially of the interaction energies. The calculations indicate further that LDA + GC should also be able to describe weaker intermolecular interactions than the usual hydrogen bond. Finally, a short discussion of the charge distribution and the dipole moments of the H₂O…?HX complexes is performed. © 1994 John Wiley & Sons, Inc.     

Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections

We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, omegaB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, omegaB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as omegaB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.     

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.     

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.