Dieter Cremer

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.

Density functional theory: coverage of dynamic and non-dynamic electron correlation effects

The electron correlation effects covered by density functional theory (DFT) can be assessed qualitatively by comparing DFT densities ρ(r) with suitable reference densities obtained with wavefunction theory (WFT) methods that cover typical electron correlation effects. The analysis of difference densities ρ(DFT)-ρ(WFT) reveals that LDA and GGA exchange (X) functionals mimic non-dynamic correlation effects in an unspecified way. It is shown that these long range correlation effects are caused by the self-interaction error (SIE) of standard X functionals. Self-interaction corrected (SIC) DFT exchange gives, similar to exact exchange, for the bonding region a delocalized exchange hole, and does not cover any correlation effects. Hence, the exchange SIE is responsible for the fact that DFT densities often resemble MP4 or MP2 densities. The correlation functional changes X-only DFT densities in a manner observed when higher order coupling effects between lower order N-electron correlation effects are included. Hybrid functionals lead to changes in the density similar to those caused by SIC-DFT, which simply reflects the fact that hybrid functionals have been developed to cover part of the SIE and its long range correlation effects in a balanced manner. In the case of spin-unrestricted DFT (UDFT), non-dynamic electron correlation effects enter the calculation both via the X functional and via the wavefunction, which may cause a double-counting of correlation effects. The use of UDFT in the form of permuted orbital and broken-symmetry DFT (PO-UDFT, BS-UDFT) can lead to reasonable descriptions of multireference systems provided certain conditions are fulfilled. More reliable, however, is a combination of DFT and WFT methods, which makes the routine description of multireference systems possible. The development of such methods implies a separation of dynamic and non-dynamic correlation effects. Strategies for accomplishing this goal are discussed in general and tested in practice for CAS (complete active space)-DFT.

Analytical evaluation of energy gradients in quadratic configuration interaction theory

Abstract Analytical formulae for the energy gradient within the quadratic configuration interaction singles and doubles (QCISD) method are derived and their implementation is discussed. The method is applied to 6–31G(d) computations on H 2 O and H 2 O 2 .

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.

Formation of OH radicals in the gas phase ozonolysis of alkenes: the unexpected role of carbonyl oxides

According to CCSD(T)/TZ + 2P calculations, the decomposition of carbonyl oxide, H2COO to HCO and OH radicals is unlikely in view of an activation enthalpy ΔΔHf0(298) of 31 kcal/mol. However, for dimethylcarbonyl oxide there is a low energy rearrangement mode (ΔΔHf0(298): 14.4 kca/mol) which involves a H atom of ghe methyl group and which leads to a hydroperoxy methyl ethene intermediate, which in turn can decompose to OH and CH2COCH3 radicals (ΔΔHf0(298): 23 kcal/mol). In the gas phase ozonolysis of alkyl substituted alkenes the formation of OH radicals is the most likely process. This has important consequences for the chemistry of the atmosphere.

A CCSD (T) investigation of carbonyl oxide and dioxirane. Equilibrium geometries, dipole moments, infrared spectra, heats of formation and isomerization energies

Abstract A CCSD and CCSD (T) investigation of carbonyl oxide (1) and its cyclic isomer dioxirane (2) has been carried out employing DZ + P and TZ + 2P basis sets. Calculated geometries, charge distributions, and dipole moments suggest that 1 possesses more zwitterionic character (CCSD (T) dipole moment 4 D) than has been predicted. 1 can be distinguished from 2 by its infrared spectrum as indicated by CCSD (T) frequencies, intensities, and isotopic shifts. The heats of formation ΔH0f (298) for 1 and 2 are 30.2 and 6.0 kcal/mol, respectively; the CCSD (T) barrier to isomerization from 1 to 2 is 19.2 kcal/mol. Decomposition of 1 and 2 can lead to CO, CO2, H2O, H2 but not to free CH2, O2 or O. Both isomers should be powerful epoxidation agents in the presence of alkenes, but they should differ in their ability to form cyclopropanes with alkenes.

Problematic p-benzyne: Orbital instabilities, biradical character, and broken symmetry

The equilibrium geometry, harmonic vibrational frequencies, and infrared transition intensities of p-benzyne were calculated at the MBPT(2), SDQ-MBPT(4), CCSD, and CCSD(T) levels of theory using different reference wave functions obtained from restricted and unrestricted Hartree-Fock (RHF and UHF), restricted Brueckner (RB) orbital, and Generalized Valence Bond (GVB) theory. RHF erroneously describes p-benzyne as a closed-shell singlet rather than a singlet biradical, which leads to orbital near-instabilities in connection with the mixing of orbital pairs b1u-ag (HOMO–LUMO), b2g-ag (HOMO-1-LUMO), and b1g-ag (HOMO-2-LUMO). Vibrational modes of the corresponding symmetries cause method-dependent anomalous increases (unreasonable force constants and infrared intensities) or decreases in the energy (breaking of the D2h symmetry of the molecular framework of p-benzyne). This basic failure of the RHF starting function is reduced by adding dynamic electron correlation. However RHF-MBPT(2), RHF-SDQ-MBPT(4), RHF-C...

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.

Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States

Computational approaches to understanding chemical reaction mechanisms generally begin by establishing the relative energies of the starting materials, transition state, and products, that is, the stationary points on the potential energy surface of the reaction complex. Examining the intervening species via the intrinsic reaction coordinate (IRC) offers further insight into the fate of the reactants by delineating, step-by-step, the energetics involved along the reaction path between the stationary states. For a detailed analysis of the mechanism and dynamics of a chemical reaction, the reaction path Hamiltonian (RPH) and the united reaction valley approach (URVA) are an efficient combination. The chemical conversion of the reaction complex is reflected by the changes in the reaction path direction t(s) and reaction path curvature k(s), both expressed as a function of the path length s. This information can be used to partition the reaction path, and by this the reaction mechanism, of a chemical reaction into reaction phases describing chemically relevant changes of the reaction complex: (i) a contact phase characterized by van der Waals interactions, (ii) a preparation phase, in which the reactants prepare for the chemical processes, (iii) one or more transition state phases, in which the chemical processes of bond cleavage and bond formation take place, (iv) a product adjustment phase, and (v) a separation phase. In this Account, we examine mechanistic analysis with URVA in detail, focusing on recent theoretical insights (with a variety of reaction types) from our laboratories. Through the utilization of the concept of localized adiabatic vibrational modes that are associated with the internal coordinates, q(n)(s), of the reaction complex, the chemical character of each reaction phase can be identified via the adiabatic curvature coupling coefficients, A(n,s)(s). These quantities reveal whether a local adiabatic vibrational mode supports (A(n,s) > 0) or resists (A(n,s) < 0) the curving of the path, and thus the structural changes of the reaction complex. URVA can show the mechanism of a reaction expressed in terms of reaction phases, revealing the sequence of chemical processes in the reaction complex and making it possible to determine those electronic factors that control the mechanism and energetics of the reaction. The magnitude of adiabatic curvature coupling coefficients is related to strength and polarizability of the bonds being broken. Transient points along the reaction path are associated with hidden intermediates and hidden transition states, which can be converted into real intermediates and transition states when the reaction conditions or the substitution pattern of the reaction complex are appropriately changed. Accordingly, URVA represents a theoretical tool with tremendous experimental potential, offering the chemist the ability to assert greater control over reactions.

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.