Search

A first-principles description of the primary photochemical processes that drive photosynthesis and sustain life on our planet remains one of the grand challenges of modern science. Recent research established that explicit incorporation of protein electrostatics in excited-state calculations of photosynthetic pigments, achieved for example with quantum-mechanics/molecular-mechanics (QM/MM) approaches, is essential for a meaningful description of the properties and function of pigment-protein complexes. Although time-dependent density functional theory has been used productively so far in QM/MM approaches for the study of such systems, this methodology has limitations. Here we pursue for the first time a QM/MM description of the reaction center in the principal enzyme of oxygenic photosynthesis, Photosystem II, using multireference wave function theory for the high-level QM region. We identify best practices and establish guidelines regarding the rational choice of active space and appropriate state-averaging for the efficient and reliable use of complete active space self-consistent field (CASSCF) and the N-electron valence state perturbation theory (NEVPT2) in the prediction of low-lying excited states of chlorophyll and pheophytin pigments. Given that the Gouterman orbitals are inadequate as a minimal active space, we define specific minimal and extended active spaces for the NEVPT2 description of electronic states that fall within the Q and B bands. Subsequently, we apply our multireference-QM/MM protocol to the description of all pigments in the reaction center of Photosystem II. The calculations reproduce the electrochromic shifts induced by the protein matrix and the ordering of site energies consistent with the identity of the primary donor (Chl D1 ) and the experimentally known asymmetric and directional electron transfer. The optimized protocol sets the stage for future multireference treatments of multiple pigments, and hence for multireference studies of charge separation, while it is transferable to the study of any photoactive embedded tetrapyrrole system.

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T 1 ) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.

Hydrated transition metal ions are prototypical systems that can be used to model properties of transition metals in complex chemical environments. These seemingly simple systems present challenges for computational chemistry and are thus crucial in evaluations of quantum chemical methods for spin-state and redox energetics. In this work, we explore the applicability of the domain-based pair natural orbital implementation of coupled cluster (DLPNO-CC) theory to the calculation of ionization energies and redox potentials for hydrated ions of all first transition row (3d) metals in the 2+/3+ oxidation states, in connection with various solvation approaches. In terms of model definition, we investigate the construction of a minimally explicitly hydrated quantum cluster with a first and second hydration layer. We report on the convergence with respect to the coupled cluster expansion and the PNO space, as well as on the role of perturbative triple excitations. A recent implementation of the conductor-like polarizable continuum model (CPCM) for the DLPNO-CC approach is employed to determine self-consistent redox potentials at the coupled cluster level. Our results establish conditions for the convergence of DLPNO-CCSD(T) energetics and stress the absolute necessity to explicitly consider the second solvation sphere even when CPCM is used. The achievable accuracy for redox potentials of a practical DLPNO-based approach is, on average, 0.13 V. Furthermore, multilayer approaches that combine a higher-level DLPNO-CCSD(T) description of the first solvation sphere with a lower-level description of the second solvation layer are investigated. The present work establishes optimal and transferable methodological choices for employing DLPNO-based coupled cluster theory, the associated CPCM implementation, and cost-efficient multilayer derivatives of the approach for open-shell transition metal systems in complex environments.

Protein-embedded chromophores are responsible for light harvesting, excitation energy transfer, and charge separation in photosynthesis. A critical part of the photosynthetic apparatus are reaction centers (RCs), which comprise groups of (bacterio)chlorophyll and (bacterio)pheophytin molecules that transform the excitation energy derived from light absorption into charge separation. The lowest excitation energies of individual pigments (site energies) are key for understanding photosynthetic systems, and form a prime target for quantum chemistry. A major theoretical challenge is to accurately describe the electrochromic (Stark) shifts in site energies produced by the inhomogeneous electric field of the protein matrix. Here, we present large-scale quantum mechanics/molecular mechanics calculations of electrochromic shifts for the RC chromophores of photosystem II (PSII) using various quantum chemical methods evaluated against the domain-based local pair natural orbital (DLPNO) implementation of the similarity-transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD). We show that certain range-separated density functionals (ωΒ97, ωΒ97X-V, ωΒ2PLYP, and LC-BLYP) correctly reproduce RC site energy shifts with time-dependent density functional theory (TD-DFT). The popular CAM-B3LYP functional underestimates the shifts and is not recommended. Global hybrid functionals are too insensitive to the environment and should be avoided, while nonhybrid functionals are strictly nonapplicable. Among the applicable approximate coupled cluster methods, the canonical versions of CC2 and ADC(2) were found to deviate significantly from the reference results both for the description of the lowest excited state and for the electrochromic shifts. By contrast, their spin-component-scaled (SCS) and particularly the scale-opposite-spin (SOS) variants compare well with the reference DLPNO-STEOM-CCSD and the best range-separated DFT methods. The emergence of RC excitation asymmetry is discussed in terms of intrinsic and protein electrostatic potentials. In addition, we evaluate a minimal structural scaffold of PSII, the D1-D2-Cyt B559 RC complex often employed in experimental studies, and show that it would have the same site energy distribution of RC chromophores as the full PSII supercomplex, but only under the unlikely conditions that the core protein organization and cofactor arrangement remain identical to those of the intact enzyme.

Face-sharing octahedral dinuclear Cr(III) compounds with d 3 -d 3 electronic configurations represent nontrivial examples of electronic complexity, posing particular challenges for theoretical and computational studies. A tris-hydroxy-bridged Cr(III)-Cr(III) system has proven to be a richly rewarding target for studies of magnetism and electron paramagnetic resonance spectroscopy. It was also reported to be a peculiarly difficult system to treat with density functional theory (DFT). In this work the magnetic coupling problem for this dimer is approached with broken-symmetry (BS)-DFT and multireference calculations that utilize the density matrix renormalization group (DMRG) to handle full-valence active spaces. BS-DFT is shown to recover the correct ordering and energy spacing of Heisenberg spin states if used in conjunction with appropriate spin projection procedures, albeit with pronounced functional sensitivity. The contrasting conclusions of previous studies are traced to incorrect inclusion of electronically excited configurations. Analysis of the direct and differential overlap of corresponding orbital pairs from the BS-DFT solution indicates that metal-metal through-space interaction is the dominant contributor to antiferromagnetic coupling. At the DFT level a procedure that utilizes pseudopotential substitution is demonstrated that allows evaluation of the direct exchange vs superexchange contributions. A complementary description is obtained with DMRG-SCF calculations that enable state-averaged CASSCF calculations with both metal and bridge orbitals in the active space. A localized orbital subspace analysis supports the DFT conclusions that in contrast to doubly bridged isoelectronic analogues, antiferromagnetic coupling in the chromium dimer arises primarily from direct metal-metal interaction but is significantly enhanced by ligand-mediated superexchange.

A test set of 12 aryl carbenes (AC12) is compiled with the purpose of establishing their adiabatic singlet-triplet energy splittings using correlated wave function based methods. The set covers both singlet and triplet ground state aryl carbenes, as well as a range of magnitudes for the ground state to excited state gap. The performance of coupled cluster methods is examined with respect to the reference wave function, the basis set, and a number of additional methodological parameters that enter the calculation. Inclusion of perturbative triples and basis set extrapolation with a combination of triple and quadruple-ζ basis sets are both required to ensure high accuracy. When canonical coupled cluster calculations become too expensive, the domain-based local pair natural orbital approach DLPNO-CCSD(T) can be used as a reliable method for larger systems, as it achieves a mean absolute error of only 0.2 kcal/mol for the singlet-triplet gaps in the present test set. Other first-principles wave function methods and selected density functional methods are also evaluated. Second-order Møller-Plesset perturbation theory approaches are only applicable in conjunction with orbital optimization (OO-MP2). Among the representative density functional methods tested, only double hybrid functionals perform sufficiently accurately to be considered useful for systems with small singlet-triplet gaps. On the basis of the reference coupled cluster results, projected gas-phase free energies are reported for all aryl carbenes. Finally, the treatment of singlet-triplet gaps in solution is discussed in terms of both implicit and explicit solvation.

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.

The calculation of redox potentials involves large energetic terms arising from gas phase ionization energies, thermodynamic contributions, and solvation energies of the reduced and oxidized species. In this work we study the performance of a wide range of wave function and density functional theory methods for the prediction of ionization energies and aqueous one-electron oxidation potentials of a set of 19 organic molecules. Emphasis is placed on evaluating methods that employ the computationally efficient local pair natural orbital (LPNO) approach, as well as several implementations of coupled cluster theory and explicitly correlated F12 methods. The electronic energies are combined with implicit solvation models for the solvation energies. With the exception of MP2 and its variants, which suffer from enormous errors arising at least partially from the poor Hartree-Fock reference, ionization energies can be systematically predicted with average errors below 0.1 eV for most of the correlated wave function based methods studies here, provided basis set extrapolation is performed. LPNO methods are the most efficient way to achieve this type of accuracy. DFT methods show in general larger errors and suffer from inconsistent behavior. The only exception is the M06-2X functional which is found to be competitive with the best LPNO-based approaches for ionization energies. Importantly, the limiting factor for the calculation of accurate redox potentials is the solvation energy. The errors in the predicted solvation energies by all continuum solvation models tested in this work dominate the final computed reduction potential, resulting in average errors typically in excess of 0.3 V and hence obscuring the gains that arise from choosing a more accurate electronic structure method.

Improved versions of the segmented all-electron relativistically contracted (SARC) basis sets for the lanthanides are presented. The second-generation SARC2 basis sets maintain efficient construction of their predecessors and their individual adaptation to the DKH2 and ZORA Hamiltonians, but feature exponents optimized with a completely new orbital shape fitting procedure and a slightly expanded f space that results in sizable improvement in CASSCF energies and in significantly more accurate prediction of spin-orbit coupling parameters. Additionally, an extended set of polarization/correlation functions is constructed that is appropriate for multireference correlated calculations and new auxiliary basis sets for use in resolution-of-identity (density-fitting) approximations in combination with both DFT and wave function based treatments. Thus, the SARC2 basis sets extend the applicability of the first-generation DFT-oriented basis sets to routine all-electron wave function-based treatments of lanthanide complexes. The new basis sets are benchmarked with respect to excitation energies, radial distribution functions, optimized geometries, orbital eigenvalues, ionization potentials, and spin-orbit coupling parameters of lanthanide systems and are shown to be suitable for the description of magnetic and spectroscopic properties using both DFT and multireference wave function-based methods.

The latest crystal structure of photosystem II at 1.9 Å resolution, which resolves the topology of the Mn4CaO5 oxygen evolving complex (OEC) at atomistic detail, enables a better correlation between structural features and spectroscopic properties than ever before. Building on the refined crystallographic model of the OEC and the protein, we present combined quantum mechanical/molecular mechanical (QM/MM) studies of the spectroscopic properties of the natural catalyst embedded in the protein matrix. Focusing on the S2 state of the catalytic cycle, we examine the convergence of not only structural parameters but also of the intracluster magnetic interactions in terms of exchange coupling constants and of experimentally relevant (55)Mn, (17)O, and (14)N hyperfine coupling constants with respect to QM/MM partitioning using five QM regions of increasing size. This enables us to assess the performance of the method and to probe second sphere effects by identifying amino acid residues that principally affect the spectroscopic properties of the OEC. Comparison between QM-only and QM/MM treatments reveals that whereas QM/MM models converge quickly to stable values, the QM cluster models need to incorporate significantly larger parts of the second coordination sphere and surrounding water molecules to achieve convergence for certain properties. This is mainly due to the sensitivity of the QM-only models to fluctuations in the hydrogen bonding network and ligand acidity. Additionally, a hydrogen bond that is typically omitted in QM-only treatments is shown to determine the hyperfine coupling tensor of the unique Mn(III) ion by regulating the rotation plane of the ligated D1-His332 imidazole ring, the only N-donor ligand of the OEC.

The performance of different wave-function-based and density functional theory (DFT) methods was evaluated with respect to the prediction of relative energies for gas-phase monosaccharide isomers. A test set of 58 structures was employed, representing all forms of isomerism encountered in d-aldohexoses. The set was built from eight hexopyranose epimers by deriving subsets of isomers that include hydroxymethyl rotamers, anomers, ring conformers, furanose, and open-chain forms. Each subset of isomers spans a different energy range and involves various stereoelectronic effects. Reference energy values were obtained with coupled-cluster calculations extrapolated to the complete basis set limit, CCSD(T)/CBS. The tested CBS-extrapolated ab initio methods include various types of Møller-Plesset (MP) perturbation theory and the localized paired natural orbital coupled electron pair approach (LPNO-CEPA). Extensive benchmarking of DFT methods was carried out with 31 functionals. The results allow us to establish a hierarchy of methods that forms a reference guide for further computational studies. Among wave-function-based methods, LPNO-CEPA proved indistinguishable from CCSD(T), offering a promising alternative for a reference method that can be applied to larger systems. MP2 and SCS-MP2 follow closely, surpassing SOS-MP2 and MP3. The mPW2PLYP-D double hybrid and the Minnesota M06-2X hybrid meta-GGA are the best performing density functionals and are directly competitive with wave-function-based ab initio methods. Among the remaining functionals, B3PW91, TPSSh, mPW1PW91, and PBE0 yield the best results on average, while PBE is the best general-purpose GGA functional, surpassing meta-GGAs and several hybrids such as B3LYP. The choice of method strongly depends on the type of isomerism that needs to be considered, since many DFT methods perform well for purely conformational isomerism, but most of them fail to describe ring versus open-chain isomerism, where LYP-based GGA functionals perform particularly poorly.

Segmented all-electron relativistically contracted (SARC) basis sets are constructed for the elements 57La-71Lu and optimized for density functional theory (DFT) applications. The basis sets are intended for use in combination with the DKH2 or ZORA scalar relativistic Hamiltonians for which individually optimized contractions are provided. Significant computational advantages can be realized owing to the loose contraction of the SARC basis sets compared to generally contracted basis sets, while their compact size allows them to replace effective core potentials for routine studies of lanthanide complexes. The new basis sets are evaluated in DFT calculations of the first four ionization energies of the lanthanides. They yield results that accurately reproduce the experimental trends, confirming a balanced treatment of different electronic configurations. The performance of the basis sets is further assessed in molecular systems with a comprehensive study of the lanthanide trihalides. Despite their compact size, the SARC basis sets demonstrate consistent, efficient, and reliable performance and will be especially useful in calculations of molecular properties that require explicit treatment of the core electrons.

A set of 41 metal-ligand bond distances in 25 third-row transition-metal complexes, for which precise structural data are known in the gas phase, is used to assess optimized and zero-point averaged geometries obtained from DFT computations with various exchange-correlation functionals and basis sets. For a given functional (except LSDA) Stuttgart-type quasi-relativistic effective core potentials and an all-electron scalar relativistic approach (ZORA) tend to produce very similar geometries. In contrast to the lighter congeners, LSDA affords reasonably accurate geometries of 5d-metal complexes, as it is among the functionals with the lowest mean and standard deviations from experiment. For this set the ranking of some other popular density functionals, ordered according to decreasing standard deviation, is BLYP > VSXC > BP86 ≈ BPW91 ≈ TPSS ≈ B3LYP ≈ PBE > TPSSh > B3PW91 ≈ B3P86 ≈ PBE hybrid. In this case hybrid functionals are superior to their nonhybrid variants. In addition, we have reinvestigated the previous test sets for 3d- (Bühl M.; Kabrede, H. J. Chem. Theory Comput. 2006, 2, 1282-1290) and 4d- (Waller, M. P.; Bühl, M. J. Comput. Chem. 2007, 28, 1531-1537) transition-metal complexes using all-electron scalar relativistic DFT calculations in addition to the published nonrelativistic and ECP results. For this combined test set comprising first-, second-, and third-row metal complexes, B3P86 and PBE hybrid are indicated to perform best. A remarkably consistent standard deviation of around 2 pm in metal-ligand bond distances is achieved over the entire set of d-block elements.

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.

In previous studies of the agostic bonding in Tp(Me2)NbCl(R'CCR' ')(R), we have made use of a hybrid QM/MM protocol (B3LYP:UFF) where the QM partition ([Nb(Cl)(iPr)(HCCH)(NHCH2)3](+)) was rather small, but the optimized structures were nevertheless in apparently good agreement with experiment. In attempting to improve this model by expanding the size of the QM region, we were surprised to discover that a full QM treatment of the whole molecule using the B3LYP functional failed to locate an agostic structure of any kind. A systematic assessment of density functionals reveals that the poor performance of B3LYP in these systems is typical of all DFT methods that do not obey the uniform electron gas (UEG) correlation limit. Those that do obey the UEG limit, in contrast, provide an excellent description of the agostic structure when the complete ligand system is treated at the QM level. The apparently good performance of our original (B3LYP:UFF) hybrid method can be traced to a cancellation of errors:  the B3LYP functional underestimates the intrinsic strength of the agostic interaction relative to competing Nb-Cl π bonding, but this is offset by an additional but unphysical electrostatic component to the agostic bond introduced by the presence of a positive charge in the QM region.