Standard Density Functional Theory Methods Research Articles

Hartree–Fock and standard density functional theory methods applied to excited states: The case of NO 2

It has been shown that energies and geometries of lowest and higher excited states of symmetric molecules can be calculated with reasonable accuracy by Hartree–Fock (HF) and standard (time-independent) density functional theory (DFT) methods. In the example of NO 2, the geometries of 15 excited doublet states in C 2 v symmetry, (1–5) 2A 2, (1–5) 2B 1, and (1–5) 2B 2 were optimized by UHF and DFT (UB3PW91) with a 6-311+G(3df) basis set, all resulting from single excitations with respect to the 2A 1 ground state. Energies and optimized geometries compare well with available literature values. Vertical HF and DFT excitation energies for these states have been compared with multireference configuration interaction and time-dependent DFT values. Examples of DFT optimized doubly and triply excited doublet states are given.

Analytic derivatives for perturbatively corrected “double hybrid” density functionals: Theory, implementation, and applications

A recently proposed new family of density functionals [S. Grimme, J. Chem. Phys. 124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to density functional theory (DFT). This fractional correlation energy is calculated at the level of second-order many-body perturbation theory (PT2) and replaces some of the semilocal DFT correlation of standard hybrid DFT methods. The new "double hybrid" functionals (termed, e.g., B2-PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchange-correlation terms in the self-consistent field operator. An implementation is reported for closed-shell as well as spin-unrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with approximately 500-600 basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2.

Electrostatics for Exploring the Nature of the Hydrogen Bonding in Polyethylene Oxide Hydration

Binding between water and models of poly(ethylene oxide), (CH2−CH2−O)n, n = 2−40, has been studied using the topographic features of the electrostatic potential, V(r), and standard density functional theory methods. It was found that, in general, the contour around the minima of the oxygen atoms overlap forming a negative-valued spiral coiled around a positive-valued helix. The positive zone defines a helical groove in the O−C−C−O units where minima lone pairs critical points are located. Topological analysis of the water molecule has also suggested that the attractive electrostatic effect between the positive water O−H zone and the negative PEO lone pairs plays an important role in the hydrogen bonding of the PEO−water system. Thus, the V(r) topology predicts a coil of water molecules around the PEO chain forming hydrogen bonding with two sites of ether oxygens. This coil is formed in such a way that more water molecules accumulate on the cavities surrounding the poly(ethylene oxide)'s oxygen atoms where...

On the performance of density functional theory for symmetry-breaking problems

Density functional theory (DFT) has been applied to three open-shell molecules (NO 3, O 4 +, and O 2 +) for which the unrestricted Hartree–Fock (UHF) wavefunction breaks spatial symmetry. In contrast to Hartree–Fock, all of the standard DFT methods we employed yielded symmetric densities for each of the molecules considered. Symmetry-broken solutions were obtained with DFT only when we used hybrid functionals including unusually large fractions of Hartree–Fock exchange. The exchange functional seems more important than the correlation functional in determining whether symmetry is preserved or broken.