Interaction energies of monosubstituted benzene dimers via nonlocal density functional theory

We present density functional calculations for the interaction energy of monosubstituted benzene dimers. Our approach utilizes a recently developed fully nonlocal correlation energy functional, which has been applied to the pure benzene dimer and several other systems with promising results. The interaction energy as a function of monomer distance was calculated for four different substituents in a sandwich and two T-shaped configurations. In addition, we considered two methods for dealing with exchange, namely, using the revPBE generalized gradient functional as well as full Hartree-Fock. Our results are compared with other methods, such as Moller-Plesset and coupled-cluster calculations, thereby suggesting the usefulness of our approach. Since our density functional based method is considerably faster than other standard methods, it provides a computationally inexpensive alternative, which is of particular interest for larger systems where standard calculations are too expensive or infeasible.     

Atomic multiplet energies from density functional calculations

Atomic multiplet term energies for dⁿ configurations have been estimated within density functional theory (DFT) exploiting symmetry to the largest possible extent. The electrostatic two-electron integrals, as well as term energies, are expressed in function of only three non-redundant single determinants (NRSDs), each of them being obtained from density functional calculations. The influence of correlation effects described with a gradient-corrected functional (GGA) is examined and discussed. Comparison with experimental data shows the reliability of this symmetry-based density functional approach.     

Nonlocal density functional calculations of the jellium metal surface

The Becke exchange functional is used for calculation of properties of the jellium model using the slab geometry inside a box with the infinite potential barriers at the boundaries. We simplify semianalytical representation of matrix elements. We calculate the surface energies and work functions with self-consistent electron densities. For all densities (here, we give results in erg/cm² for r_s = 2.07 bohr, in comparison with the LSD approximation (?602)) and the uncorrected Pw GGA -II (?730), the Becke-II exchange only (?1212), and the Becke-II exchange with Perdew86 correlation (?830) [always close to Pw GGA -I (?814)] give smaller surface energies. The most important factor determining values of surface energies from different GGAS seems to be a form of a correlation potential. We also calculate the effect of finite slab thickness and the vacuum region thickness on the surface energy at the LSD level and indicate its importance in various jellium model calculations. © 1995 John Wiley & Sons, Inc.     

Electron density distribution in stacked benzene dimers: a new approach towards the estimation of stacking interaction energies

The potential energy surface for the benzene dimer in stacked conformations (84 points calculated) was computed at the MP2(FC)6-31+G(2d,2p) level of theory. Electron density (ED) distribution computed using the MP2(FC), B3LYP, and Hartree-Fock methods with the same basis set is studied in the frame of topological analysis. It is found that ED topology does not depend on the method of calculation. The values of the ED and its Laplacian in the cage critical point calculated using different methods are determined to be linearly dependent with the slope depending on basis set. Correlation equations based on these properties allow the interaction energy between benzene rings to be predicted with 8% mean relative error in the energy for the given region of the potential energy surface. This provides a new method for the estimation of stacking interaction energy using ED properties calculated with low level quantum-chemical methods.     

Theoretical Auger electron spectra of polymers by density functional theory calculations using model dimers

We propose a new approach for analysis of Auger electron spectra (AES) of polymers by density functional theory (DFT) calculations with the Slater's transition-state concept. Simulated AES and X-ray photoelectron spectra (XPS) of four polymers [(CH2CH2)n (PE), (CH2CH(CH3))n (PP), (CH2CH(OCH3))n (PVME), and (CH2CH(COCH3))n (PVMK)] by DFT calculations using model dimers are in a good accordance with the experimental ones. The experimental AES of the polymers can be classified in each range of 1s-2p2p, 1s-2s2p, and 1s-2s2s transitions for C KVV and O KVV spectra, and in individual contributions of the functional groups from the theoretical analysis.     

Density functional calculations of surface free energies

We propose a general method of thermodynamic integration to find the free energy of a surface, where our integration parameter is taken to be the strain on the unit cell of the system (which in the example presented in this paper is simply the extension of the unit cell along the normal to the surface), and the integration is performed over the thermal average stress from a molecular dynamics run. In order to open up a vacuum gap in a continuous and reversible manner, an additional control interaction has been introduced. We also use temperature integration to find a linear relation for the temperature dependence of the free surface energy. These methods have been applied to the titanium dioxide (110) surface, using first principles density functional theory. A proof of principle calculation for zero temperature shows excellent agreement between the integral calculation and the difference in energy calculated by the DFT program. Calculations that have been performed at 295 and 1000 K give excellent agreement between the two integration methods.     

Kinetic energies to analyze the experimental auger electron spectra by density functional theory calculations

In the Auger electron spectra (AES) simulations, we define theoretical modified kinetic energies of AES in the density functional theory (DFT) calculations. The modified kinetic energies correspond to two final-state holes at the ground state and at the transition-state in DFT calculations, respectively. This method is applied to simulate Auger electron spectra (AES) of 2nd periodic atom (Li, Be, B, C, N, O, F)-involving substances (LiF, beryllium, boron, graphite, GaN, SiO₂, PTFE) by deMon DFT calculations using the model molecules of the unit cell. Experimental KVV (valence band electrons can fill K-shell core holes or be emitted during KVV-type transitions) AES of the (Li, O) atoms in the substances agree considerably well with simulation of AES obtained with the maximum kinetic energies of the atoms, while, for AES of LiF, and PTFE substance, the experimental F KVV AES is almost in accordance with the spectra from the transitionstate kinetic energy calculations.     

Ab initio and density functional calculations of mean-square amplitudes of vibration for benzene and cubane

Mean-square amplitudes of vibration were calculated using ab initio and density functional methods for benzene and cubane. Both 6-31G^* and 6-311G^** basis sets were employed. It was found that significant improvements were achieved when electron correlation was introduced, even if only at the local density functional level. The mean-square amplitudes calculated were not effected by the basis set used for benzene and slightly improved for the highly strained cubane molecule when the larger basis set was used. An attempt was also made to improve the calculated mean-square amplitudes by making use of scale factors found in the literature, which were developed to improve the calculated frequencies. It was found that only the SCF mean-square amplitudes were significantly improved.     

Communication: Avoiding unbound anions in density functional calculations

Converged approximate density functional calculations usually do not bind anions due to large self-interaction error. But Hartree-Fock (HF) calculations have no such problem, producing negative HOMO energies. Thus, electron affinities can be calculated from density functional total energy differences using approximations such as PBE and B3LYP, evaluated on HF densities (for both anion and neutral). This recently proposed scheme is shown to work very well for molecules, better than the common practice of restricting the basis set except for cases such as CN, where the HF density is too inaccurate due to spin contamination.     

Nonlocal van der Waals density functional: the simpler the better

We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.     

Orbital-shell density functional in calculations on the intramolecular and intermolecular potentials for chromium atoms and benzene molecules

Calculations have been performed in the orbital-shell density-functional approximation from the nonempirical approximating quasiparticle density function, which show that the total potential energy surface for the CrBz complex is described by a two-well interaction potential. The minimum in the short-range part of the potential corresponds to an intramolecular bond in a bisarenechromium charge-transfer complex, while the minimum in the long-range part describes the molecular interaction between those components in atomically dispersed solutions of chromium in arene matrices. Good agreement with experiment is obtained.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 2, pp. 218–220, March–April, 1990.     

Spin-multiplet energies from time-dependent density functional theory

Starting from a formally exact density-functional representation of the frequency-dependent linear density response and exploiting the fact that the latter has poles at the true excitation energies, we develop a density-functional method for the calculation of excitation energies. Simple additive corrections to the Kohn-Sham single-particle transition energies are derived whose actual computation only requires the ordinary static Kohn-Sham orbitals and the corresponding eigenvalues. Numerical results are presented for spin-singlet and triplet energies. © 1996 John Wiley & Sons, Inc.     

Modeling proton transfer in imidazole-like dimers: a density functional theory study

A detailed theoretical study of proton transfer reaction in protonated imidazole, 1,2,3-triazole, and tetrazole dimers, the basic components of polymeric membrane used in proton exchange membranes fuel cells, has been carried out. In particular, several approaches based on density functional theory have been considered and their results compared with those provided by post-HF methods. From a computational point of view, these molecules appear to be a very challenging playground also for robust and recent functionals. Indeed none of the considered approaches provide results in close agreement with the reference post-HF data and a combined BMK//B3LYP model seems the only approach able to reproduce both the energetic and the structural features. From a chemical point of view, two new mechanisms of proton transfer in tetrazole dimers have been investigated and found to be more favorable than that previously hypothesized in literature. At the same time, the theoretical results show a direct connection between the obtained proton transfer barrier and the charge localized on the transferred hydrogen.     

Cluster free energies and nucleation: a density functional approach

Density functional methods of statistical mechanics are applied to calculate the average density profiles and free energies of small (50–500 particles) liquid clusters in unstable or metastable equilibrium with respect to the vapor. The results are compared with those obtained from experiments on homogeneous nucleation of liquids from the vapor.     

Quantum Monte Carlo calculations of the dissociation energies of three-electron hemibonded radical cationic dimers

We report variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the dissociation energies of the three-electron hemibonded radical cationic dimers of He, NH3, H2O, HF, and Ne. These systems are particularly difficult for standard density-functional methods such as the local-density approximation and the generalized gradient approximation. We have performed both all-electron (AE) and pseudopotential (PP) calculations using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. Our results are in good agreement with coupled-cluster CCSD(T) calculations. We have also studied the relative stability of the hemibonded and hydrogen-bonded water radical dimer isomers. Our calculations indicate that the latter isomer is more stable, in agreement with post-Hartree-Fock methods. The excellent agreement between our AE and PP results demonstrates the high quality of the PPs used within our VMC and DMC calculations.     

Origin of the surprising enhancement of electrostatic energies by electron-donating substituents in substituted sandwich benzene dimers

A recent study of substituted face-to-face benzene dimers by Lewis and co-workers [J. Am. Chem. Soc. 2011, 133, 3854-3862] indicated a surprising enhancement of electrostatic interactions for both electron-withdrawing and electron-donating substituents. Here we demonstrate that charge penetration (an attractive electrostatic interaction arising from the overlap of the electron densities on the two monomers) is the cause of this counterintuitive effect. These charge penetration effects are significant at typical π-π interaction distances, and they are not easily described by multipole models. A simple measure of a substituent's electron-donating or electron-withdrawing character, such as the Hammett parameter σ(m), is unlikely to capture subtle charge penetration effects. Indeed, correlation of the relative total energies or relative electrostatic energies with ∑σ(m) breaks down for multiply substituted face-to-face benzene dimers.     

Molecular binding energies from partition density functional theory

Approximate molecular calculations via standard Kohn-Sham density functional theory are exactly reproduced by performing self-consistent calculations on isolated fragments via partition density functional theory [P. Elliott, K. Burke, M. H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010)]. We illustrate this with the binding curves of small diatomic molecules. We find that partition energies are in all cases qualitatively similar and numerically close to actual binding energies. We discuss qualitative features of the associated partition potentials.