Frank Neese

The ORCA program system

ORCA is a general‐purpose quantum chemistry program package that features virtually all modern electronic structure methods (density functional theory, many‐body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger molecules, transition metal complexes, and their spectroscopic properties. ORCA uses standard Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.

All-Electron Scalar Relativistic Basis Sets for Third-Row Transition Metal Atoms.

A family of segmented all-electron relativistically contracted (SARC) basis sets for the elements Hf-Hg is constructed for use in conjunction with the Douglas-Kroll-Hess (DKH) and zeroth-order regular approximation (ZORA) scalar relativistic Hamiltonians. The SARC basis sets are loosely contracted and thus offer computational advantages compared to generally contracted relativistic basis sets, while their sufficiently small size allows them to be used in place of effective core potentials (ECPs) for routine studies of molecules. Practical assessments of the SARC basis sets in DFT calculations of atomic (ionization energies) as well as molecular properties (geometries and bond dissociation energies for MHn complexes) confirm that the basis sets yield accurate and reliable results, providing a balanced description of core and valence electron densities. CCSD(T) calculations on a series of gold diatomic compounds also demonstrate the applicability of the basis sets to correlated methods. The SARC basis sets will be of most utility in calculating molecular properties for which the core electrons cannot be neglected, such as studies of electron paramagnetic resonance, Mössbauer and X-ray absorption spectra, and topological analysis of electron densities.

X-ray Emission Spectroscopy Evidences a Central Carbon in the Nitrogenase Iron-Molybdenum Cofactor

A central light atom in a cofactor at the nitrogenase active site is identified as a carbon. Nitrogenase is a complex enzyme that catalyzes the reduction of dinitrogen to ammonia. Despite insight from structural and biochemical studies, its structure and mechanism await full characterization. An iron-molybdenum cofactor (FeMoco) is thought to be the site of dinitrogen reduction, but the identity of a central atom in this cofactor remains unknown. Fe Kβ x-ray emission spectroscopy (XES) of intact nitrogenase MoFe protein, isolated FeMoco, and the FeMoco-deficient ∆nifB protein indicates that among the candidate atoms oxygen, nitrogen, and carbon, it is carbon that best fits the XES data. The experimental XES is supported by computational efforts, which show that oxidation and spin states do not affect the assignment of the central atom to C4–. Identification of the central atom will drive further studies on its role in catalysis.

An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix.

A straightforward modification of the resolution of the identity (RI) approximation to the Coulomb interaction is described. In the limit of basis sets that are dominated by high angular momentum functions the observed speedups in realistic test systems reach a factor of 2 compared to the standard RI algorithm, and a factor of up to 300 compared to the standard algorithm to form the Coulomb matrix. More moderate savings on the order of 0–20% are obtained for the more commonly used smaller basis sets. A series of test calculations is reported to illustrate the efficiency of the algorithm.

Prediction of electron paramagnetic resonance g values using coupled perturbed Hartree–Fock and Kohn–Sham theory

A method for calculating the EPR g-tensor based on coupled perturbed Hartree–Fock (HF) and density functional theory (DFT) is presented. The one-electron molecular orbitals of a spin- unrestricted Slater determinant are calculated up to first order in the applied magnetic field. The g-tensor is evaluated as a mixed second derivative property with respect to the applied field and the electron magnetic moment. Thus, spin-polarization and spin–orbit coupling are simultaneously included in the calculation. The treatment focuses on orbitally nondegenerate molecules but is valid for a general ground state spin S and, for the first time, it is possible to include hybrid density functionals in the treatment. The relativistic mass and diamagnetic gauge corrections are also considered. An implementation of the theory is described. Extensive numerical calculations for a series of small molecules are reported with the Hartree–Fock (HF) method, the local density approximation (LSD), the generalized gradient approximat...

Natural triple excitations in local coupled cluster calculations with pair natural orbitals

In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calculation of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calculations on alkane chains. The accuracy of the DLPNO-CCSD(T) approximation relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an average error of approximately 0.5 kcal∕mol for a challenging test set of medium sized organic molecules. The triples correction typically adds 30%-50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addition to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calculation on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions.

Slow magnetization dynamics in a series of two-coordinate iron(II) complexes

A series of two-coordinate complexes of iron(II) were prepared and studied for single-molecule magnet behavior. Five of the compounds, Fe[N(SiMe3)(Dipp)]2 (1), Fe[C(SiMe3)3]2 (2), Fe[N(H)Ar′]2 (3), Fe[N(H)Ar*]2 (4), and Fe(OAr′)2 (5) feature a linear geometry at the FeII center, while the sixth compound, Fe[N(H)Ar#]2 (6), is bent with an N–Fe–N angle of 140.9(2)° (Dipp = C6H3-2,6-Pri2; Ar′ = C6H3-2,6-(C6H3-2,6-Pri2)2; Ar* = C6H3-2,6-(C6H2-2,4,6-Pri2)2; Ar# = C6H3-2,6-(C6H2-2,4,6-Me3)2). Ac magnetic susceptibility data for all compounds revealed slow magnetic relaxation under an applied dc field, with the magnetic relaxation times following a general trend of 1 > 2 > 3 > 4 > 5 ≫ 6. Arrhenius plots created for the linear complexes were fit by employing a sum of tunneling, direct, Raman, and Orbach relaxation processes, resulting in spin reversal barriers of Ueff = 181, 146, 109, 104, and 43 cm−1 for 1–5, respectively. CASSCF/NEVPT2 calculations on the crystal structures were performed to explore the influence of deviations from rigorous D∞h geometry on the d-orbital splittings and the electronic state energies. Asymmetry in the ligand fields quenches the orbital angular momentum of 1–6, but ultimately spin–orbit coupling is strong enough to compensate and regenerate the orbital moment. The lack of simple Arrhenius behavior in 1–5 can be attributed to a combination of the asymmetric ligand field and the influence of vibronic coupling, with the latter possibility being suggested by thermal ellipsoid models to the diffraction data.

Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method

Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Moller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol(-1). Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chemical applications.

Prediction and interpretation of the 57Fe isomer shift in mössbauer spectra by density functional theory

Abstract The calibration of two popular density functionals (B3LYP and BP86) for the prediction of isomer shifts (IS) in 57 Fe Mossbauer (MB) spectra is reported. A linear correlation between non-relativistically calculated theoretical electron densities and experimentally measured ISs is established. Both functionals lead to accurate predictions of MB ISs with standard deviations on the order of approximately 0.1 mm s −1 over a range of approximately 2 mm s −1 . The correlation holds for complexes of different total charge, total spin, valence state at the iron, coordination number and coordination geometry. A detailed analysis of the contributions to the IS is presented. It is shown that the important contributions are: (a) the variation of the 3s-contribution which is mainly caused by differing shielding according to the d-population of the metal; and (b) variations in the valence shell contribution. The latter contribution accounts for approximately 70% of the totally observed variation. The interpretation of the valence contribution is complex and involves contributions from changes in covalencies, orbital distortions due to bonding and shielding effects. The changes in metalligand distances are also an important factor, which influences the shape of the 4s-orbital and therefore modulates ISs.

Biological Water Oxidation

Photosystem II (PSII), a multisubunit pigment-protein supercomplex found in cyanobacteria, algae, and plants, catalyzes a unique reaction in nature: the light-driven oxidation of water. Remarkable recent advances in the structural analysis of PSII now give a detailed picture of the static supercomplex on the molecular level. These data provide a solid foundation for future functional studies, in particular the mechanism of water oxidation and oxygen release. The catalytic core of the PSII is a tetramanganese-calcium cluster (Mn₄O₅Ca), commonly referred to as the oxygen-evolving complex (OEC). The function of the OEC rests on its ability to cycle through five metastable states (Si, i = 0-4), transiently storing four oxidizing equivalents, and in so doing, facilitates the four electron water splitting reaction. While the latest crystallographic model of PSII gives an atomic picture of the OEC, the exact connectivity within the inorganic core and the S-state(s) that the X-ray model represents remain uncertain. In this Account, we describe our joint experimental and theoretical efforts to eliminate these ambiguities by combining the X-ray data with spectroscopic constraints and introducing computational modeling. We are developing quantum chemical methods to predict electron paramagnetic resonance (EPR) parameters for transition metal clusters, especially focusing on spin-projection approaches combined with density functional theory (DFT) calculations. We aim to resolve the geometric and electronic structures of all S-states, correlating their structural features with spectroscopic observations to elucidate reactivity. The sequence of manganese oxidations and concomitant charge compensation events via proton transfer allow us to rationalize the multielectron S-state cycle. EPR spectroscopy combined with theoretical calculations provides a unique window into the tetramangenese complex, in particular its protonation states and metal ligand sphere evolution, far beyond the scope of static techniques such as X-ray crystallography. This approach has led, for example, to a detailed understanding of the EPR signals in the S₂-state of the OEC in terms of two interconvertible, isoenergetic structures. These two structures differ in their valence distribution and spin multiplicity, which has important consequences for substrate binding and may explain its low barrier exchange with solvent water. New experimental techniques and innovative sample preparations are beginning to unravel the complex sequence of substrate uptake/inclusion, which is coupled to proton release. The introduction of specific site perturbations, such as replacing Ca²⁺ with Sr²⁺, provides discrete information about the ligand environment of the individual Mn ions. In this way, we have identified a potential open coordination site for one Mn center, which may serve as a substrate binding site in the higher S-states, such as S₃ and S₄. In addition, we can now monitor the binding of the substrate water in the lower S-states (S₁ and S₂) using new EPR-detected NMR spectroscopies. These studies provided the first evidence that one of the substrates is subsumed into the complex itself and forms an oxo-bridge between two Mn ions. This result places important new restrictions on the mechanism of O-O bond formation. These new insights from natures water splitting catalyst provide important criteria for the rational design of bioinspired synthetic catalysts.