Tom Ziegler

Chemistry with ADF

We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order‐N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency‐dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF‐typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation‐strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time‐dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena.

The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration

An algorithm, based on numerical integration, has been proposed for the evaluation of analytical energy gradients within the Hartree–Fock–Slater (HFS) method. The utility of this algorithm in connection with molecular structure optimization is demonstrated by calculations on organics, main group molecules, and transition metal complexes. The structural parameters obtained from HFS calculations are in at least as good agreement with experiment as structures obtained from ab initio HF calculations. The time required to evaluate the energy gradient by numerical integration constitutes only a fraction (40%–25%) of the elapsed time in a full HFS‐SCF calculation. The algorithm is also suitable for density functional methods with exchange‐correlation potential different from that employed in the HFS method.

On the calculation of multiplet energies by the hartree-fock-slater method

It is shown that a consistent application of the p1/3 approximation of the Hartree-Fock-Slater method requires the use of one specific procedure, the sum method, for the calculation of the energy Es1of singlet excited states of closed shell molecules. Further, Es1is found to be in reasonable agreement with experiment for a number of molecules, contrary to the energy Es2obtained according to another method discussed in the literature. The calculation of other multiplet splittings than singlet-triplet in the Hartree-Fock-Slater method is also considered.

A Combined Charge and Energy Decomposition Scheme for Bond Analysis

UNLABELLED In the present study we have introduced a new scheme for chemical bond analysis by combining the Extended Transition State (ETS) method [ Theor. Chim. Acta 1977, 46, 1 ] with the Natural Orbitals for Chemical Valence (NOCV) theory [ J. Phys. Chem. A 2008, 112, 1933 ; J. Mol. MODEL 2007, 13, 347 ]. The ETS-NOCV charge and energy decomposition scheme based on the Kohn-Sham approach makes it not only possible to decompose the deformation density, Δρ, into the different components (such as σ, π, δ, etc.) of the chemical bond, but it also provides the corresponding energy contributions to the total bond energy. Thus, the ETS-NOCV scheme offers a compact, qualitative, and quantitative picture of the chemical bond formation within one common theoretical framework. Although, the ETS-NOCV approach contains a certain arbitrariness in the definition of the molecular subsystems that constitute the whole molecule, it can be widely used for the description of different types of chemical bonds. The applicability of the ETS-NOCV scheme is demonstrated for single (H3X-XH3, for X = C, Si, Ge, Sn) and multiple (H2X═XH2, H3CX≡XCH3, for X = C, Ge) covalent bonds between main group elements, for sextuple and quadruple bonds between metal centers (Cr2, Mo2, W2, [Cl4CrCrCl4](4-)), and for double bonds between a metal and a main group element ((CO)5Cr═XH2, for X = C, Si, Ge, Sn). We include finally two applications involving hydrogen bonding. The first covers the adenine-thymine base pair and the second the interaction between C-H bonds and the metal center in the alkyl complex.

Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules

We report the implementation of the computation of rotatory strengths, based on time-dependent density functional theory, within the Amsterdam Density Functional program. The code is applied to the simulation of circular dichroism spectra of small and moderately sized organic molecules, such as oxiranes, aziridines, cyclohexanone derivatives, and helicenes. Results agree favorably with experimental data, and with theoretical results for molecules that have been previously investigated by other authors. The efficient algorithms allow for the simulation of CD spectra of rather large molecules at a reasonable accuracy based on first-principles theory. The choice of the Kohn–Sham potential is a critical issue. It is found that standard gradient corrected functionals often yield the correct shape of the spectrum, but the computed excitation energies are systematically underestimated for the samples being studied. The recently developed exchange-correlation potentials “GRAC” and “SAOP” often yield much better a...

Calculation of DFT-GIAO NMR shifts with the inclusion of spin-orbit coupling

A formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors, based on density functional theory (DFT), is presented. Scalar-relativistic and spin-orbit coupling effects are taken into account, and a Fermi-contact term is included in the NMR shielding tensor expression. Gauge-including atomic orbitals (GIAO) and a frozen-core approximation are used. This formulation has been implemented, and 1H and 13C NMR shifts of hydrogen and methyl halides have been calculated and show good agreement with experiment. 13C NMR shifts of 5d transition metal carbonyls have been calculated and show improved agreement with experiment over previous scalar-relativistic calculations. For the metal carbonyls it is shown explicitly that the combination of spin-orbit coupling and magnetic field mixes spin triplet states into the ground state, inducing a spin density that then interacts with the nuclei of the metal carbonyl via the Fermi-contact term. Results indicate that the Fermi-contact contribution ...

Bond Orbitals from Chemical Valence Theory

Two sets of orbitals are derived, directly connected to the Nalewajski-Mrozek valence and bond-multiplicity indices: Localized Orbitals from the Bond-Multiplicity Operator (LOBO) and the Natural Orbitals for Chemical Valence (NOCV). LOBO are defined as the eigenvectors of the bond-multiplicity operator. The expectation value of this operator is the corresponding bond index. Thus, the approach presented here allows for a discussion of localized orbitals and bond multiplicity within one common framework of chemical valence theory. Another set of orbitals discussed in the present work, NOCV, are defined as eigenvectors of the overall chemical valence operator. This set of orbitals can be especially useful for a description of bonding in transition metal complexes, as it allows for separation of the deformation density contributions originating from the ligand --> metal donation and metal --> ligand back-donation.

Calculation of NMR shielding tensors based on density functional theory and a scalar relativistic Pauli-type Hamiltonian. The application to transition metal complexes

This article deals with the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy based on a scalar relativistic two-component Pauli-type Hamiltonian. A complete formulation of the method within the framework of the gauge including atomic orbitals (GIAO) is given. Further, an implementation, based on density functional theory (DFT) is presented. The new method is applied to the 17O shielding in transition-metal oxo complexes [MO4]n- (M = Cr, Mo, W; Mn, Tc, Rh; Ru, Os) and to the metal chemical shift in transition-metal carbonyls M(CO)6 (M = Cr, Mo, W). This represents the first calculation of heavy-element shifts that is based on a relativistic first-principle quantum mechanical method. The inclusion of relativity is crucial for a proper description of ligand and metal shieldings in 5d complexes, but it is also important in 4d complexes. Limitations of the method, among them the neglect of the spin-orbit coupling, are discussed in detail.

Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential

In this study we have introduced a formulation of time-dependent density functional theory (TDDFT) based on a noncollinear exchange-correlation potential. This formulation is a generalization of conventional TDDFT. The form of this formulation is exactly the same as that of the conventional TDDFT for the excitation energies of transitions that do not involve spin flips. In addition, this noncollinear TDDFT formulation allows for spin-flip transitions. This feature makes it possible to resolve more fully excited state spin multiplets, while for closed-shell systems, the spin-flip transitions will result in singlet-triplet excitations and this excitation energy calculated from this formulation of TDDFT is exactly the same as that from ordinary TDDFT. This formulation is applied to the dissociation of H(2) in its (1)Sigma(g) (+) ground state and (1)Sigma(u) (+) and (3)Sigma(u) (-) excited states with (3)Sigma(u) (-) (M(s)=+1) as the reference state and the multiplets splitting of some atoms.

Nuclear spin–spin coupling constants from regular approximate relativistic density functional calculations. I. Formalism and scalar relativistic results for heavy metal compounds

We present a relativistic formulation of the spin–spin coupling hyperfine terms based on the two component zeroth-order regular approximate Hamiltonian. The scalar relativistic parts of the resulting operators were used for an implementation into the Amsterdam density functional program. Application of the code for the calculation of one-bond metal-ligand couplings of systems containing 183W, 195Pt, 199Hg, and 207Pb shows that scalar relativistic calculations are able to reproduce major parts of the relativistic effects on the coupling constants, which can be even larger in magnitude than the respective total nonrelativistic values. The spatial origin of the regular approximate relativistic analogue of the Fermi-contact contribution, which is usually responsible for the strong relativistic increase of the couplings, is analyzed. Its relativistic effects can be described by the relativistic increase of valence orbital density in the very vicinity of the heavy nucleus.