Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals

Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Method for Electronic Excited States: A Benchmark Study

The recently developed second-order perturbation theory restricted active space (RASPT2) method has been benchmarked versus the well-established complete active space (CASPT2) approach. Vertical excitation energies for valence and Rydberg excited states of different groups of organic (polyenes, acenes, heterocycles, azabenzenes, nucleobases, and free base porphin) and inorganic (nickel atom and copper tetrachloride dianion) molecules have been computed at the RASPT2 and multistate (MS) RASPT2 levels using different reference spaces and compared with CASPT2, CCSD, and experimental data in order to set the accuracy of the approach, which extends the applicability of multiconfigurational perturbation theory to much larger and complex systems than previously. Relevant aspects in multiconfigurational excited state quantum chemistry such as the valence-Rydberg mixing problem in organic molecules or the double d-shell effect for first-row transition metals have also been addressed.

Structural, spectroscopic, and multiconfigurational quantum chemical investigations of the electron-rich metal-metal triple-bonded Tc(2)X(4)(PMe(3))(4) (X = Cl, Br) complexes

The compounds Tc(2)Cl(4)(PMe(3))(4) and Tc(2)Br(4)(PMe(3))(4) were formed from the reaction between (n-Bu(4)N)(2)Tc(2)X(8) (X = Cl, Br) and trimethylphosphine. The Tc(II) dinuclear species were characterized by single-crystal XRD, UV-visible spectroscopy, and cyclic voltammetry techniques, and the results are compared to those obtained from density functional theory and multiconfigurational (CASSCF/CASPT2) quantum chemical studies. The compound Tc(2)Cl(4)(PMe(3))(4) crystallizes in the monoclinic space group C2/c [a = 17.9995(9) A, b = 9.1821(5) A, c = 17.0090(9) A, beta = 115.4530(10) degrees ] and is isostructural to M(2)Cl(4)(PMe(3))(4) (M = Re, Mo, W) and to Tc(2)Br(4)(PMe(3))(4). The metal-metal distance (2.1318(2) A) is similar to the one found in Tc(2)Br(4)(PMe(3))(4) (2.1316(5) A). The calculated molecular structures of the ground states are in excellent agreement with the structures determined experimentally. Calculations of effective bond orders for Tc(2)X(8)(2-) and Tc(2)X(4)(PMe(3))(4) (X = Cl, Br) indicate stronger pi bonds in the Tc(2)(4+) core than in Tc(2)(6+) core. The electronic spectra were recorded in benzene and show a series of low intensity bands in the range 10 000-26 000 cm(-1). Assignment of the bands as well as computing their excitation energies and intensities were performed at both TD-DFT and CASSCF/CASPT2 levels of theory. Calculations predict that the lowest energy band corresponds to the delta* --> sigma* transition, the difference between calculated and experimental values being 228 cm(-1) for X = Cl and 866 cm(-1) for X = Br. The next bands are attributed to delta* --> pi*, delta --> sigma*, and delta --> pi* transitions. The cyclic voltammograms exhibit two reversible waves and indicate that Tc(2)Br(4)(PMe(3))(4) exhibits more positive oxidation potentials than Tc(2)Cl(4)(PMe(3))(4.) This phenomenon is discussed and ascribed to stronger metal (d) to halide (d) back bonding in the bromo complex. Further analysis indicates that Tc(II) dinuclear species containing pi-acidic phosphines are more difficult to oxidize, and a correlation between oxidation potential and phosphine acidity was established.

MOLCAS 7: the next generation

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies.

Three- and four-body nonadditivities in nucleic acid tetramers: a CCSD(T) study

Three- and four-body nonadditivities in the uracil tetramer (in DNA-like geometry) and the GC step (in crystal geometry) were investigated at various levels of the wave-function theory: HF, MP2, MP3, L-CCD, CCSD and CCSD(T). All of the calculations were performed using the 6-31G**(0.25,0.15) basis set, whereas the HF, MP2 and the MP3 nonadditivities were, for the sake of comparison, also determined with the much larger aug-cc-pVDZ basis set. The HF and MP2 levels do not provide reliable values for many-body terms, making it necessary to go beyond the MP2 level. The benchmark CCSD(T) three- and four-body nonadditivities are reasonably well reproduced at the MP3 level, and almost quantitative agreement is obtained (fortuitously) either on the L-CCD level or as an average of the MP3 and the CCSD results. Reliable values of many-body terms (especially their higher-order correlation contributions) are obtained already when the rather small 6-31G**(0.25,0.15) basis set is used. The four-body term is much smaller when compared to the three-body terms, but it is definitely not negligible, e.g. in the case of the GC step it represents about 16% of all of the three- and four-body terms. While investigating the geometry dependence of many-body terms for the GG step at the MP3/6-31G**(0.25,0.15) level, we found that it is necessary to include at least three-body terms in the determination of optimal geometry parameters.

Calculation of protein-ligand interaction energies by a fragmentation approach combining high-level quantum chemistry with classical many-body effects

We have developed a method to estimate accurate interaction energies between a full protein and a bound ligand. It is based on the recently proposed PMISP (polarizable multipole interaction with supermolecular pairs) method (Soderhjelm, P.; Ryde, U. J. Phys. Chem. A 2009, 113, 617), which treats electrostatic interaction by multipoles up to quadrupoles, induction by anisotropic polarizabilities, and nonclassical interactions by explicit quantum mechanical (QM) calculations, using a fragmentation approach. For a whole protein, electrostatics and induction are treated the same way, but for the nonclassical interactions, a Lennard-Jones term from a standard molecular mechanics (MM) force field (e.g., Amber) is used outside a certain distance from the ligand (4-7 A). This QM/MM variant of the PMISP method is carefully tested by varying this distance. Several approximations related to the classical interactions are also evaluated. It is found that one can speed up the calculation by using density functional theory to compute multipoles and polarizabilities but that a proper treatment of polarization is important. As a demonstration of the method, the interaction energies of two ligands bound to avidin are calculated at the MP2/aug-cc-pVTZ level, with an expected relative error of 1-2%.

Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.

Reaction mechanism of manganese superoxide dismutase studied by combined quantum and molecular mechanical calculations and multiconfigurational methods

Manganese superoxide dismutases (MnSODs) are enzymes that convert two molecules of the poisonous superoxide radical into molecular oxygen and hydrogen peroxide. During the reaction, the manganese ion cycles between the Mn(2+) and Mn(3+) oxidation states and accomplishes its enzymatic action in two half-cycles (corresponding to the oxidation and reduction of O(2)(-)). Despite many experimental and theoretical studies dealing with SODs, including quantum chemical active-site-model studies of numerous variants of the reaction mechanisms, several details of MnSOD enzymatic action are still unclear. In this study, we have modeled and compared four reaction pathways (one associative, one dissociative, and two second-sphere) in a protein environment using the QM/MM approach (combined quantum and molecular mechanics calculations) at the density functional theory level. The results were complemented by CASSCF/CASPT2/MM single-point energy calculations for the most plausible models to account properly for the multireference character of the various spin multiplets. The results indicate that the oxidation of O(2)(-) to O(2) most likely occurs by an associative mechanism following a two-state (quartet-octet) reaction profile. The barrier height is estimated to be less than 25 kJ.mol(-1). On the other hand, the conversion of O(2)(-) to H(2)O(2) is likely to take place by a second-sphere mechanism, that is, without direct coordination of the superoxide radical to the manganese center. The reaction pathway involves the conical intersection of two quintet states, giving rise to an activation barrier of approximately 60 kJ.mol(-1). The calculations also indicate that the associative mechanism can represent a competitive pathway in the second half-reaction with the overall activation barrier being only slightly higher than the activation barrier in the second-sphere mechanism. The activation barriers along the proposed reaction pathways are in very good agreement with the experimentally observed reaction rates of SODs (k(cat) approximately 10(4)-10(5) s(-1)).

How accurate can a force field become? A polarizable multipole model combined with fragment-wise quantum-mechanical calculations

A new method to accurately estimate the interaction energy between a large molecule and a smaller ligand is presented. The method approximates the electrostatic and induction contributions classically by multipole and polarizability expansions, but uses explicit quantum-mechanical fragment calculations for the remaining (nonclassical) contributions, mainly dispersion and exchange repulsion. Thus, it represents a limit of how accurate a force field can ever become for interaction energies if pairwise additivity of the nonclassical term is assumed (e.g., all general-purpose force fields). The accuracy is tested by considering protein-ligand model systems for which the true MP2/6-31G* interaction energies can be computed. The method is shown to be more accurate than related fragmentation approaches. The remaining error (2-5 and approximately10 kJ/mol for neutral and charged ligands, respectively) can be decreased by including the polarizing effect from surrounding fragments in the quantum-mechanical calculations.

Generating Cu(II)-oxyl/Cu(III)-oxo species from Cu(I)-alpha-ketocarboxylate complexes and O2: in silico studies on ligand effects and C-H-activation reactivity

A mechanism for the oxygenation of Cu(I) complexes with alpha-ketocarboxylate ligands that is based on a combination of density functional theory and multireference second-order perturbation theory (CASSCF/CASPT2) calculations is elaborated. The reaction proceeds in a manner largely analogous to those of similar Fe(II)-alpha-ketocarboxylate systems, that is, by initial attack of a coordinated oxygen molecule on a ketocarboxylate ligand with concomitant decarboxylation. Subsequently, two reactive intermediates may be generated, a Cu-peracid structure and a [CuO](+) species, both of which are capable of oxidizing a phenyl ring component of the supporting ligand. Hydroxylation by the [CuO](+) species is predicted to proceed with a smaller activation free energy. The effects of electronic and steric variations on the oxygenation mechanisms were studied by introducing substituents at several positions of the ligand backbone and by investigating various N-donor ligands. In general, more electron donation by the N-donor ligand leads to increased stabilization of the more Cu(II)/Cu(III)-like intermediates (oxygen adducts and [CuO](+) species) relative to the more Cu(I)-like peracid intermediate. For all ligands investigated, the [CuO](+) intermediates are best described as Cu(II)-O(*-) species with triplet ground states. The reactivity of these compounds in C-H abstraction reactions decreases with more electron-donating N-donor ligands, which also increase the Cu-O bond strength, although the Cu-O bond is generally predicted to be rather weak (with a bond order of about 0.5). A comparison of several methods to obtain singlet energies for the reaction intermediates indicates that multireference second-order perturbation theory is likely more accurate for the initial oxygen adducts, but not necessarily for subsequent reaction intermediates.

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-mu-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.