Jürgen Gräfenstein

Nuclear magnetic resonance spin–spin coupling constants from coupled perturbed density functional theory

For the first time, a complete implementation of coupled perturbed density functional theory (CPDFT) for the calculation of NMR spin–spin coupling constants (SSCCs) with pure and hybrid DFT is presented. By applying this method to several hydrides, hydrocarbons, and molecules with multiple bonds, the performance of DFT for the calculation of SSCCs is analyzed in dependence of the XC functional used. The importance of electron correlation effects is demonstrated and it is shown that the hybrid functional B3LYP leads to the best accuracy of calculated SSCCs. Also, CPDFT is compared with sum-over-states (SOS) DFT where it turns out that the former method is superior to the latter because it explicitly considers the dependence of the Kohn–Sham operator on the perturbed orbitals in DFT when calculating SSCCs. The four different coupling mechanisms contributing to the SSCC are discussed in connection with the electronic structure of the molecule.

The combination of density functional theory with multi-configuration methods - CAS-DFT

Abstract CAS-DFT is presented as a method that allows an economical simultaneous treatment of static and dynamic correlation effects in molecules with multi-reference character. Central problems of CAS-DFT concern the double counting of dynamic correlation effects and the choice of the proper input quantities for the DFT functional. Also, the question of treating both active and inactive orbitals in a consistent way is discussed. Test calculations with CAS-DFT for the ring opening of dioxirane and the excitation energies of methylene prove that the method works reasonably.

An efficient algorithm for the density-functional theory treatment of dispersion interactions

The quasi-self-consistent-field dispersion-corrected density-functional theory formalism (QSCF-DC-DFT) is developed and presented as an efficient and reliable scheme for the DFT treatment of van der Waals dispersion complexes, including full geometry optimizations and frequency calculations with analytical energy derivatives in a routine way. For this purpose, the long-range-corrected Perdew-Burke-Ernzerhof exchange functional and the one-parameter progressive correlation functional of Hirao and co-workers are combined with the Andersson-Langreth-Lundqvist (ALL) long-range correlation functional. The time-consuming self-consistent incorporation of the ALL term in the DFT iterations needed for the calculation of forces and force constants is avoided by an a posteriori evaluation of the ALL term and its gradient based on an effective partitioning of the coordinate space into global and intramonomer coordinates. QSCF-DC-DFT is substantially faster than SCF-DC-DFT would be. QSCF-DC-DFT is used to explore the potential energy surface (PES) of the benzene dimer. The results for the binding energies and intermolecular distances agree well with coupled-cluster calculations at the complete basis-set limit. We identify 16 stationary points on the PES, which underlines the usefulness of analytical energy gradients for the investigation of the PES. Furthermore, the inclusion of analytically calculated zero point energies reveals that large-amplitude vibrations connect the eight most stable benzene dimer forms and make it difficult to identify a dominating complex form. The tilted T structure and the parallel-displaced sandwich form have the same D(0) value of 2.40 kcal/mol, which agrees perfectly with the experimental value of 2.40+/-0.40 kcal/mol.

Symmetric Halogen Bonding Is Preferred in Solution

Halogen bonding is a recently rediscovered secondary interaction that shows potential to become a complementary molecular tool to hydrogen bonding in rational drug design and in material sciences. Whereas hydrogen bond symmetry has been the subject of systematic studies for decades, the understanding of the analogous three-center halogen bonds is yet in its infancy. The isotopic perturbation of equilibrium (IPE) technique with (13)C NMR detection was applied to regioselectively deuterated pyridine complexes to investigate the symmetry of [N-I-N](+) and [N-Br-N](+) halogen bonding in solution. Preference for a symmetric arrangement was observed for both a freely adjustable and for a conformationally restricted [N-X-N](+) model system, as also confirmed by computation on the DFT level. A closely attached counterion is shown to be compatible with the preferred symmetric arrangement. The experimental observations and computational predictions reveal a high energetic gain upon formation of symmetric, three-center four-electron halogen bonding. Whereas hydrogen bonds are generally asymmetric in solution and symmetric in the crystalline state, the analogous bromine and iodine centered halogen bonds prefer symmetric arrangement in solution.

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.

Development of a CAS-DFT method covering non-dynamical and dynamical electron correlation in a balanced way

CAS-DFT (Complete Active Space Density Functional Theory) is presented as a method that allows an economical, simultaneous treatment of non-dynamical and dynamical correlation effects for electronic systems with multi-reference character. Central problems of CAS-DFT concern the effective coupling between wave function and DFT method, the double counting of dynamical correlation effects, the choice of the proper input quantities for the DFT functional, the balanced treatment of core and active orbital correlation, of equal-spin and opposite-spin correlation effects, and the inclusion of spin polarization to handle closed- and open-shell systems in a balanced way. We present CAS-DFT2(CS,SPP,FOS,DS) (CAS-DFT using level 2 for the distinction of core and active orbital correlations, carried out with the Colle–Salvetti functional, using the Stoll–Pavlidou–Preuss functional for equal-spin correlation corrections, including spin polarization in the scaling procedure, and correcting with the Davidson–Staroverov density for low-spin cases). The method is free of any self-interaction error and size extensive provided the active space is properly chosen. For the three lowest states of methylene, stringent and less stringent tests are used to demonstrate the performance of the new CAS-DFT method for six different active spaces.

Calculation and analysis of NMR spin–spin coupling constants

The analysis of NMR spin-spin coupling leads to a unique insight into the electronic structure of closed-shell molecules, provided one is able to decode the different features of the spin-spin coupling mechanism. For this purpose, the physics of spin-spin coupling is described and the way how spin-spin coupling constants (SSCCs) can be quantum mechanically determined. Based on this insight, a set of requirements is derived that guide the development of a quantum mechanical analysis of spin-spin coupling. It is demonstrated that the J-OC-PSP (=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization) analysis method fulfills all requirements. J-OC-PSP makes it possible to partition the isotropic indirect SSCC J or its reduced analogue K as well as the four Ramsey terms (Fermi contact (FC), spin dipole (SD), diamagnetic spin orbit (DSO), paramagnetic spin orbit (PSO)) leading to J (or K) into Cartesian components (for the anisotropic Ramsey terms SD, DSO, PSO), orbital contributions or electron interaction terms. For the purpose of decoding the spin-spin coupling mechanism, FC, SD, DSO, and PSO coupling is discussed in detail and related to electronic and bonding features of the molecules in question. The myth of empirical and semiempirical relationships between SSCCs and bonding features is unveiled. It is found that most relationships are only of limited, partly dubious value, often arising from a fortuitous cancellation of terms that cannot be expected in general. These relationships are replaced by quantum chemical relations and descriptions that directly reflect the complex electronic processes leading to spin-spin coupling.

On the diagnostic value of (Ŝ2) in Kohn-Sham density functional theory

Unrestricted density functional theory (UDFT) is, in addition to its application to high spin multiplet systems, an efficient method for describing singlet biradical states. In this connection, spin contamination of the UDFT description as measured by the expectation values of Ŝ2 is of interest, but is difficult to assess since the calculation of (Ŝ2) as the expectation value of a twoparticle operator is not possible within the single-determinant approach of DFT. A new way of determining (Ŝ2) from the UDFT (UHF or any other) spin magnetization density (SMD) ms (r) = pα(r) −pβ(r) is described and applied to the stretched H2 molecule and the singlet state of the para-didehydrobenzene biradical for a number of different functionals. Although (Ŝ2) as calculated from the Kohn-Sham determinant is found to differ significantly from the corresponding value obtained with the help of the SMD in the case of singlet biradicals, the former result is a diagnostic value and can be used to assess spin contamination of the UDFT description on a qualitative basis.

Can density functional theory describe multi-reference systems? Investigation of carbenes and organic biradicals

Kohn–Sham (KS) density functional theory (DFT) in its present approximate form cannot be applied to electron systems with strong multi-reference character. Various ways are discussed to develop DFT for multi-reference systems. The restricted open-shell singlet (ROSS) formalism is a modification of the conventional open-shell KS formalism, which makes a reliable, but still economical treatment of open-shell singlet biradicals possible. The complete-active-space DFT (CAS-DFT) method combines an explicit treatment of multi-configurational character with the DFT treatment of dynamic electron correlation effects. Due to the flexibility in the choice of the active space, this method is in principle appropriate for all kinds of multi-reference problems. Based on sample calculations for carbenes and organic biradicals, the advantages and limitations of ROSS-DFT and CAS-DFT are discussed. Some possibilities for future improvements of DFT methods for multi-reference problems are pointed out.