Dimitrios G. Liakos

Efficient and accurate local single reference correlation methods for high-spin open-shell molecules using pair natural orbitals

A production level implementation of the high-spin open-shell (spin unrestricted) single reference coupled pair, quadratic configuration interaction and coupled cluster methods with up to doubly excited determinants in the framework of the local pair natural orbital (LPNO) concept is reported. This work is an extension of the closed-shell LPNO methods developed earlier [F. Neese, F. Wennmohs, and A. Hansen, J. Chem. Phys. 130, 114108 (2009); F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009)]. The internal space is spanned by localized orbitals, while the external space for each electron pair is represented by a truncated PNO expansion. The laborious integral transformation associated with the large number of PNOs becomes feasible through the extensive use of density fitting (resolution of the identity (RI)) techniques. Technical complications arising for the open-shell case and the use of quasi-restricted orbitals for the construction of the reference determinant are discussed in detail. As in the closed-shell case, only three cutoff parameters control the average number of PNOs per electron pair, the size of the significant pair list, and the number of contributing auxiliary basis functions per PNO. The chosen threshold default values ensure robustness and the results of the parent canonical methods are reproduced to high accuracy. Comprehensive numerical tests on absolute and relative energies as well as timings consistently show that the outstanding performance of the LPNO methods carries over to the open-shell case with minor modifications. Finally, hyperfine couplings calculated with the variational LPNO-CEPA∕1 method, for which a well-defined expectation value type density exists, indicate the great potential of the LPNO approach for the efficient calculation of molecular properties.

Weak Molecular Interactions Studied with Parallel Implementations of the Local Pair Natural Orbital Coupled Pair and Coupled Cluster Methods.

A parallel implementation of the recently developed local pair natural orbital coupled electron pair approximation (LPNO-CEPA/n, n = Version 1, 2, or 3) and the corresponding LPNO coupled cluster method with single- and double excitations (LPNO-CCSD) is described. A detailed analysis alongside pseudocode is presented for the most important computational steps. The scaling with respect to the number of processors is reasonable and speedups of about 10 with 14 processors have been found in benchmark calculations (wall-clock time). The most important factor limiting the efficiency of the scaling with respect to the number of processors is probably the limited bandwidth of the presently prevailing multicore machines. The parallel LPNO methods were applied to study weak intermolecular interactions. Initially, the well-established S22 set of molecules was studied. The mean absolute error resulting from the use of the LPNO-CEPA/1 method relative to the most recent CCSD(T) reference data is found to be 0.24 kcal/mol. Thus, LPNO-CEPA/1 holds great promise for the efficient ab initio treatment of weak intermolecular interactions. In order to demonstrate the applicability of the methods to real systems, a two-dimensional potential energy surface for a trimer of 2,4-dihydroxy-3-acetyl-6-methyl acetophenone [C11H12O4] (81 atoms, 1296 basis functions, 133 single points) has been calculated with the LPNO-CEPA/1 method. In this system, a clear distinction can be made between hydrogen bonding and π-π interactions. The global minimum on the PES obtained from the calculations agrees excellently with the experimentally determined crystal structure. By contrast, popular density functional methods show no discernible minimum.

Interplay of Correlation and Relativistic Effects in Correlated Calculations on Transition-Metal Complexes: The (Cu2O2)(2+) Core Revisited.

Owing to the availability of large-scale computing facilities and the development of efficient new algorithms, wave function-based ab initio calculations are becoming more common in bioinorganic chemistry. In principle they offer a systematic route toward high accuracy. However, these calculations are by no means trivial. In this contribution we address some pertinent points through a systematic theoretical study for the equilibrium between the peroxo- and bis-(μ-oxo) isomers of the [{Cu(C2H8N2)}2O2](2+) complex. While this system is often regarded as a prototypical multireference case, we treat it with the single reference local-pair natural orbital coupled cluster method and reiterate that the multireference character in this system is very limited. A set of intermediate structures, for the interconversion between the two isomers, is calculated through a relaxed surface scan thus allowing the calculation of an energetic profile that cleanly connects the bis-(μ-oxo) and side-on peroxo minima on the ground-state potential energy surface. Only at the highest level of theory involving complete basis set extrapolation, triple excitation contributions as well as relativistic and solvent effects, the bis-(μ-oxo) isomer is found to be slightly more stable than the peroxo structure. This is in agreement with the experimental findings. The effects of basis set, triples excitation, relativity, and solvent contribution have all been analyzed in detail. Finally, the ab initio results are compared with density functional calculations using various functionals. It is demonstrated that the largest part of the discrepancies of the results reported in the literature are due to an inconsistent handling of relativistic effects, which are large in both ab initio and density functional theory calculations.

Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory.

The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDFs) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.

A Multiconfigurational ab Initio Study of the Zero-Field Splitting in the Di- and Trivalent Hexaquo-Chromium Complexes

A detailed analysis of the value of zero-field splitting for the di- and trivalent chromium hexaquo complexes is presented. The effect of the Jahn-Teller distortion was studied, for the case of the divalent complex, through the use of state-averaged CASSCF calculations, for the mapping of the potential energy surface along the e(g) normal modes. At the minima of the surface, multiconfigurational ab initio calculations (spectroscopy oriented configuration interaction, SORCI, and difference dedicated configuration interaction, DDCI) were used for the calculation of the D tensor and the analysis of the individual contributions to it. The final value calculated with the SORCI method (D = -2.45 cm(-1)) for the divalent complex is in excellent agreement with the experimental estimate (D = -2.3 cm(-1)). The importance of inclusion of the direct spin-spin coupling contribution to D is pointed out ( approximately 16%). At the same time, contributions of the higher than the lowest (3)T(1g) triplets were found to be non-negligible as well ( approximately 11%). The accuracy of second-order perturbation theory for the calculation of SOC was investigated and found to be satisfactory. For comparison, DFT calculations were performed with hybrid (B3LYP) and nonhybrid (BP86) functionals and were found to be inferior to the wave function based ab initio methods.

Correlated wavefunction methods in bioinorganic chemistry

In this commentary the challenges faced in the application of wavefunction-based ab initio methods to (open-shell) transition metal complexes of (bio)inorganic interest are briefly touched on. Both single-reference and multireference methods are covered. It is stressed that the generation and nature of the reference wavefunction is a subject of major importance. How erroneous results can be easily obtained even with coupled-cluster theory is illustrated through the example of the septet–quintet separation in iron(IV)–oxo complexes. Second, the interplay between relativistic and correlation effects is important. This is demonstrated with coupled-cluster calculations on models for dinuclear copper active sites, where relativity has a major influence on the relative stabilities of the bis(μ-oxo) and side-on peroxo species.

Domain Based Pair Natural Orbital Coupled Cluster Studies on Linear and Folded Alkane Chains.

In this study the question of what is the last unbranched alkane that prefers a linear conformation over a folded one is revisited from a theoretical point of view. Geometries have been optimized carefully using the most accurate theoretical approach available to date for such systems, namely, doubly hybrid density functional theory in conjunction with larger quadruple-ζ quality basis sets. The resulting geometries deviate significantly from previously reported ones and have a significant impact on the predicted energetics. Electronic energies were calculated using the efficient and accurate domain local pair natural orbital coupled cluster method with single-, double-, and triple substitutions (DLPNO-CCSD(T)) electronic structure method. Owing to the methods efficiency, we were able to employ up to quadruple-ζ quality basis sets for all hydrocarbons up to C19H40. In conjunction with carefully designed basis set extrapolation techniques, it is estimated that the electronic energies reported in this study deviate less than 1 kJ/mol from the canonical CCSD(T) basis set limit. Thermodynamic corrections were calculated with the PW6B95-D3 functional and the def2-QZVP basis set. Our prediction is that the last linear conformer is either C16H34 or C17H36 with the latter being more probable. C18H38 can be safely ruled out as the most stable isomer at 100 K. These findings are in agreement with the elegant experimental studies of Suhm and co-workers. Deviations between the current and previous theoretical results are analyzed in detail.

Dealing with Complexity in Open-Shell Transition Metal Chemistry from a Theoretical Perspective: Reaction Pathways, Bonding, Spectroscopy, And Magnetic Properties

Publisher Summary This chapter illustrate the challenges that are met in theoretical transition metal chemistry: (1) reactivity of high-valent iron-oxo sites and the challenge of multiple spin-state channels; (2) The treatment of magnetic spectroscopic observables in the case of (near) orbital degeneracy; (3) The experimentally validated description of transition metal complexes with coordinated ligand radicals; (4) The calculation of the magnetic properties of oligonuclear transition metal clusters with applications to Photosystem II. The subjects treated in the chapter are related to the fact that open-shell transition metals display a high degree of electronic complexity. This shows up in their reaction pathway that will frequently show multistate reactivity. Likewise, the magnetic and electronic properties of open-shell transition metals can be very complicated, as the case of Jahn Teller systems, and special techniques need to be employed to successfully model them. The intricate bonding situations that are created by exchange coupling (in essence, nothing but a very weak chemical bond) in metal radical systems and oligonuclear metal clusters are another area that is highly challenging to theory.

Theoretical elucidation of a classic reaction: protonation of the quadruple bond of the octachlorodimolybdate(II,II) [Mo2Cl8]4- anion.

The protonation reaction of the unbridged quadruple metal-metal bond of [Mo(2)Cl(8)](4-) anion producing the triply bonded hydride [Mo(2)(μ-H)(μ-Cl)(2)Cl(6)](3-) is studied by accurate Density Functional Theory computations. The reactant, product, stable intermediates, and transition states are located on the potential energy surface. The water solvent is explicitly included in the calculations. Full reaction profiles are calculated and compared to experimental data. The mechanism of the reaction is fully elucidated. This involves two steps. The first is a proton transfer from an oxonium ion to the quadruple bond, being rate determining. The second, involves the internal rearrangement of chlorine atoms and is much faster. Activation energies with a mean value of 19 kcal/mol are calculated, in excellent agreement with experimental values.