Elfi Kraka

Electron correlation and the self-interaction error of density functional theory

The self-interaction error (SIE) of commonly used DFT functionals has been systematically investigated by comparing the electron density distribution ρ(r) generated by self-interaction corrected DFT (SIC-DFT) with a series of reference densities obtained by DFT or wavefunction theory (WFT) methods that cover typical electron correlation effects. Although the SIE of GGA functionals is considerably smaller than that of LDA functionals, it has significant consequences for the coverage of electron correlation effects at the DFT level of theory. The exchange SIE mimics long range (non-dynamic) pair correlation effects, and is responsible for the fact that the electron density of DFT exchange-only calculations resembles often that of MP4, MP2 or even CCSD(T) calculations. Changes in the electron density caused by SIC-DFT exchange are comparable with those that are associated with HF exchange. Correlation functionals contract the density towards the bond and the valence region, thus taking negative charge out of the van der Waals region where these effects are exaggerated by the influence of the SIE of the correlation functional. Hence, SIC-DFT leads in total to a relatively strong redistribution of negative charge from van der Waals, non-bonding, and valence regions of heavy atoms to the bond regions. These changes, although much stronger, resemble those obtained when comparing the densities of hybrid functionals such as B3LYP with the corresponding GGA functional BLYP. Hence, the balanced mixing of local and non-local exchange and correlation effects as it is achieved by hybrid functionals mimics SIC-DFT and can be considered as an economic way to include some SIC into standard DFT. However, the investigation shows also that the SIC-DFT description of molecules is unreliable because the standard functionals used were optimized for DFT including the SIE.

The impact of the self-interaction error on the density functional theory description of dissociating radical cations: ionic and covalent dissociation limits.

Self-interaction corrected density functional theory was used to determine the self-interaction error for dissociating one-electron bonds. The self-interaction error of the unpaired electron mimics nondynamic correlation effects that have no physical basis where these effects increase for increasing separation distance. For short distances the magnitude of the self-interaction error takes a minimum and increases then again for decreasing R. The position of the minimum of the magnitude of the self-interaction error influences the equilibrium properties of the one-electron bond in the radical cations H2+ (1), B2H4+ (2), and C2H6+ (3), which differ significantly. These differences are explained by hyperconjugative interactions in 2 and 3 that are directly reflected by the self-interaction error and its orbital contributions. The density functional theory description of the dissociating radical cations suffers not only from the self-interaction error but also from the simplified description of interelectronic exchange. The calculated differences between ionic and covalent dissociation for 1, 2, and 3 provide an excellent criterion for determining the basic failures of density functional theory, self-interaction corrected density functional theory, and other methods. Pure electronic, orbital relaxation, and geometric relaxation contributions to the self-interaction error are discussed. The relevance of these effects for the description of transition states and charge transfer complexes is shown. Suggestions for the construction of new exchange-correlation functionals are given. In this connection, the disadvantages of recently suggested self-interaction error-free density functional theory methods are emphasized.

Density functional theory for open-shell singlet biradicals

The description of open-shell singlet OSS s-p biradicals by density functional theory DFT requires at least a . two-configurational TC or, in general, a MC-DFT approach, which bears many unsolved problems. These can be avoided . by reformulating the TC description in the spirit of restricted open shell theory for singlets ROSS and developing an exchange-correlation functional for ROSS-DFT. ROSS-DFT turns out to lead to reliable descriptions of geometry and . vibrational frequencies for OSS biradicals. The relative energies of the OSS states obtained at the ROSS-B3LYPr6-311G d,p level are often better than the corresponding ROSS-MP2 results. However, in those cases where spin polarization in a conjugated p systems plays a role, DFT predicts the triplet state related to the OSS state 2-4 kcalrmol too stable. q 1998 Elsevier Science B.V. All rights reserved.

Some Thoughts about Bond Energies, Bond Lengths, and Force Constants

Abstract The bond energy (BE) of a polyatomic molecule cannot be measured and, therefore, determination of BEs can only be done within a model using a set of assumptions. The bond strength is reflected by the intrinsic BE (IBE), which is related to the intrinsic atomization energy (IAE) and which represents the energy of dissociation under the provision that the degree of hybridization is maintained for all atoms of the molecule. IBE and BE differ in the case of CC and CH bonds by the promotion, the hybridization, and the charge reorganization energy of carbon. Since the latter terms differ from molecule to molecule, IBE and BE are not necessarily parallel and the use of BEs from thermochemical models can be misleading. The stretching force constant is a dynamical quantity and, therefore, it is related to the bond dissociation energy (BDE). Calculation and interpretation of stretching force constants for local internal coordinate modes are discussed and it is demonstrated that the best relationship between BDEs and stretching force constants is obtained within the model of adiabatic internal modes. The valence stretching force constants are less suitable since they are related to an artificial bond dissociation process with geometrical relaxation effects suppressed, which leads to an intrinsic BDE (IBDE). In the case of AXn molecules, symmetric coordinates can be used to get an appropriate stretching force constant that is related to the BE. However, in general stretching force constants determined for symmetry coordinates do not reflect the strength of a particular bond since the related dissociation processes are strongly influenced by the stability of the products formed.

Characterization of CF bonds with multiple-bond character: bond lengths, stretching force constants, and bond dissociation energies.

Isoelectronic C=F(+) and C=O bonds contained in fluoro-substituted carbenium ions, aldehydes, and ketones are investigated with regard to their bond properties by utilizing the vibrational spectra of these molecules. It is demonstrated that bond dissociation energies (BDEs), bond lengths, vibrational stretching frequencies, and bond densities are not reliable descriptors of the bond strength. The latter is related to the intrinsic BDE, which corresponds to nonrelaxed dissociation products retaining the electronic structure and geometry they have in the molecule. It is shown that the harmonic stretching force constants k(a) of the localized internal coordinate vibrations (adiabatic vibrational modes) reflect trends in the intrinsic BDEs. The k(a) values of both CO and CF bonds are related to the bond lengths through a single exponential function. This observation is used to derive a common bond order n for 46 CO- and CF-containing molecules that reliably describes differences in bonding. CF bonds in fluorinated carbenium ions possess bond orders between 1.3 and 1.7 as a result of significant pi back-bonding from F to C, which is sensitive to electronic effects caused by substituents at the carbenium center. Therefore, the strength of the C=F(+) bond can be used as a sensor for (hyper)conjugation and other electronic effects influencing the stability of the carbenium ion. The diatomic C=F(+) ion has a true double bond due to pi donation from the F atom. The characterization of CF bonds with the help of adiabatic stretching modes is also applied to fluoronium ions (n = 0.3-0.6) and transition states involving CF cleavage and HF elimination (n = 0.7-0.8).

Bonding in Mercury Molecules Described by the Normalized Elimination of the Small Component and Coupled Cluster Theory

Bond dissociation energies (BDEs) of neutral HgX and cationic HgX(+) molecules range from less than a kcal mol(-1) to as much as 60 kcal mol(-1). Using NESC/CCSD(T) [normalized elimination of the small component and coupled-cluster theory with all single and double excitations and a perturbative treatment of the triple excitations] in combination with triple-zeta basis sets, bonding in 28 mercury molecules HgX (X = H, Li, Na, K, Rb, CH(3), SiH(3), GeH(3), SnH(3), NH(2), PH(2), AsH(2), SbH(2), OH, SH, SeH, TeH, O, S, Se, Te, F, Cl, Br, I, CN, CF(3), OCF(3)) and their corresponding 28 cations is investigated. Mercury undergoes weak covalent bonding with its partner X in most cases (exceptions: X = alkali atoms, which lead to van der Waals bonding) although the BDEs are mostly smaller than 12 kcal mol(-1). Bonding is weakened by 1) a singly occupied destabilized sigma*-HOMO and 2) lone pair repulsion. The magnitude of sigma*-destabilization can be determined from the energy difference BDE(HgX)-BDE(HgX(+)), which is largest for bonding partners from groups IVb and Vb of the periodic table (up to 80 kcal mol(-1)). BDEs can be enlarged by charge transfer from Hg and increased HgX ionic bonding, provided the bonding partner of Hg is sufficiently electronegative. The fine-tuning of covalent and ionic bonding, sigma-destabilization, and lone-pair repulsion occurs via relativistic effects where 6s AO contraction and 5d AO expansion are decisive. Lone pair repulsion involving the mercury 5d AOs plays an important role in the case of some mercury chalcogenides HgE (E = O, Te) where it leads to (3)Pi rather than (1)Sigma(+) ground states. However, both HgE((3)Pi) and HgE((1)Sigma(+)) should not be experimentally detectable under normal conditions, which is in contrast to experimental predictions suggesting BDE values for HgE between 30 and 53 kcal mol(-1). The results of this work are discussed with regard to their relevance for mercury bonding in general, the chemistry of mercury, and reactions of elemental Hg in the atmosphere.

Effect of the self-interaction error for three-electron bonds: On the development of new exchange-correlation functionals

The dissociation behavior as well as the equilibrium properties of radical cations with three-electron bonds, namely He2+˙, N2H6+˙, O2H4+˙, F2H2+˙, and Ne2+˙ are investigated using standard and self-interaction-corrected density functional theory (SIC-DFT) in connection with a variety of pure and hybrid exchange-correlation (XC) functionals. The impact of the self-interaction error (SIE) on the results of standard DFT is analyzed considering the individual orbital contributions to the SIE, the dependence of the SIE on the separation distance between the dissociation fragments, and its impact on the equilibrium properties of 2–6. A local analysis of the SIE in terms of exact and DFT exchange holes reveals that the SIE mimics not only non-dynamic but also an increasing amount of dynamic electron correlation effects as the number of valence electrons is enlarged. Standard DFT describes the dissociation of three-electron bonds qualitatively incorrectly. This can be traced back in the first instance to the SIE of the bonding β electron, which mimics a spurious long-range correlation with a non-existing delocalized α electron in the same bond. A comparison of the covalent (symmetric) and ionic (symmetry-broken) state of radical cations 2–6 at large interaction distances provides further insight in the inconsistencies of the DFT description: (i) Not only the SIE but also the approximate description of the interelectronic exchange contributes to the incorrect description of the dissociation. (ii) Dissociating three-electron bonds show a specific form of long-range correlation effects, which is neither accounted for by standard DFT, SIC-DFT nor Hartree–Fock theory. Indeed, SIC-DFT provides a qualitatively better description of the dissociation of radical cations, however in general a poor performance when describing equilibrium properties. There is no need for SIC-DFT methods. Instead, there is need for XC functionals with exact exchange and long-range correlation effects (e.g. mimicked by the exchange SIE) absorbed in the correlation functional. Implications of our findings for the construction of new density functionals are discussed.

m-Benzyne and bicyclo[3.1.0]hexatriene – which isomer is more stable? – a quantum chemical investigation

Abstract Density functional theory (DFT) predicts that bicyclo[3.1.0]hexatriene ( 2 ) is more stable than its isomer m -benzyne ( 1 ). Hess [Eur. J. Org. Chem. (2001) 2185] has argued that experimental findings suggesting 1 can equally or even better be associated with 2 . However, high level ab initio calculations (CCSD(T), CASPT2) show that 2 does not exist and that the previously measured infrared spectrum is correctly assigned to 1 . Bond stretch isomers are possible for p -benzynes but not for m -benzynes. The electrophilic character of m -benzynes is in line with 1 but not with 2 .

Influence of the self-interaction error on the structure of the DFT exchange hole

Abstract Approximate density functional theory (DFT) covers long-range non-dynamic electron correlation via the exchange functional while the correlation functional includes just the short-range dynamic electron correlation effects. We show that the self-interaction error of approximate exchange functionals (local density approximation, LDA and others) mimics the long-range correlation effects. For this purpose the exchange hole is investigated at the Hartree–Fock, the LDA, and the self-interaction corrected (SIC)-LDA levels of theory.

What correlation effects are covered by density functional theory

The electron density distribution ρ(r) generated by a DFT calculation was systematically studied by comparison with a series of reference densities obtained by wavefunction theory (WFT) methods that cover typical electron correlation effects. As a sensitive indicator for correlation effects the dipole moment of the CO molecule was used. The analysis reveals that typical LDA and GGA exchange functional already simulate effects that are actually reminiscent of pair and three-electron correlation effects covered by MP2, MP4, and CCSD(T) in WFT. Correlation functionals contract the density towards the bond and the valence region thus taking negative charge out of the van der Waals region. It is shown that these improvements are relevant for the description of van der Waals interactions. Similar to certain correlated single-determinant WFT methods, BLYP and other GGA functionals underestimate ionic terms needed for a correct description of polar bonds. This is compensated for in hybrid functionals by mixing in HF exchange. The balanced mixing of local and non-local exchange and correlation effects leads to the correct description of polar bonds as in the B3LYP description of the CO molecule. The density obtained with B3LYP is closer to CCSD and CCSD(T) than to MP2 or MP4, which indicates that the B3LYP hybrid functional mimics those pair and three-electron correlation effects, which in WFT are only covered by coupled cluster methods.