The main features of the ultraviolet spectrum of acrolein have been studied by a multireference perturbative treatment and by a time dependent density functional approach. The valence and Rydberg transition energies have been calculated and the assignment of the experimental bands has been clarified. The different relaxation trends of the three lowest singlet and triplet excited states have been analyzed by unconstrained geometry optimizations. This has allowed, in particular, the characterization of a twisted (3)(pipi*) state, which is crucial for the interesting photophysics and photochemistry of the acrolein molecule and, more generally, of the alpha,beta-enones. Solvatochromic shifts in aqueous solution have been investigated using a combined discrete/continuum approach based on the so called polarizable continuum model. The experimental trends are well reproduced by this approach and a closer degeneracy in the triplet manifold has been detected in solution with respect to gas phase.

The ultraviolet spectrum of acetone in vacuum and in aqueous solution has been computed by different quantum mechanical methods coupled to the polarizable continuum model (PCM) for describing bulk solvent effects. The results in vacuo show that the time-dependent density functional theory (TDDFT) approach using the PBE0 functional reproduces quite well the result obtained at the CASPT2 level. Supermolecule computations confirm that water molecules belonging to the first shell of polar groups ( here the carbonyl oxygen) must be explicitly included in the quantum mechanical treatment, whereas the effect of other solvent molecules ( which is far from being negligible) can be reliably described by the PCM. Moreover, statistical averaging effects have been taken into account by performing canonical molecular dynamics (MD) simulations followed by TDDFT quantum mechanical computations on representative clusters of increasing dimensions immersed in a polarizable continuum. The results show that the combined MD/DFT/PCM approach is reliable and effective, although the performances of the force field used in the MD simulations must be further investigated.

In this Letter, we report the electronic spectrum of the allyl radical, obtained with multiconfigurational perturbation theory (MS-CASPT2). The assignment of the spectrum is in accordance with experiment to within 0.2 eV. We have computed the complete first Rydberg series and the beginning of the second Rydberg series. A new valence-excited B-2(1) state has been found which has hitherto been hidden by Rydberg transitions. A rationalisation of the electronic spectrum is provided in terms of resonance forms in ground and excited states. This model shows that while a multiconfigurational wavefunction is necessary to qualitatively model the system, the large ionic character of the valence electronic states makes an accurate treatment of the dynamical correlation necessary for a quantitative description of the spectrum.

The electronic structure and low-lying electronic states of a Co-III(diiminato)(NPh) complex have been studied using mulficonfigurational wave function theory (CASSCF/CASPT2) The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

The scaled opposite spin second-order Moller-Plesset (SOS-MP2) energy expression is reformulated using Cholesky decomposition of the amplitude matrix. The resulting algorithm requires an auxiliary basis or Cholesky representation of the two-electron integrals and shows fourth-order scaling with system size. Based on an analysis of operation counts, we estimate that the present approach is computationally advantageous compared to the analogous fourth-order algorithms that employ Laplace transforms.

We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals (”Cholesky molecular orbitals”) demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implementation scales cubically, the algorithm is significantly faster than any of the conventional localization schemes. In addition, since this approach does not require starting orbitals, it will be useful in local correlation treatments on top of diagonalization-free Hartree-Fock optimization algorithms.

At variance, with most of the quantum chemistry software presently available, MOLCAS is a package that is specialized in multiconfigurational wave function theory (MC-WFT) rather than density functional theory (DFT). Given the much higher algorithmic complexity of MC-WFT versus DFT, an extraordinary effort needs to be made from the programming point of view to achieve state-of-the-art performance for large-scale calculations. In particular, a robust and efficient implementation of the Cholesky decomposition techniques for handling two-electron integrals has been developed which is unique to MOLCAS. Together with this 'Cholesky infrastructure', a powerful and multilayer graphical and scripting user interface is available, which is an essential ingredient for the setup of MC-WFT calculations. These two aspects of the MOLCAS software constitute the focus of the present report.

A method is suggested which allows truncation of the virtual space in Cholesky decomposition-based multiconfigurational perturbation theory (CD-CASPT2) calculations with systematic improvability of the results. The method is based on a modified version of the frozen natural orbital (FNO) approach used in coupled cluster theory. The idea is to exploit the near-linear dependence among the eigenvectors of the virtual-virtual block of the second-order Moller-Plesset density matrix. It is shown that FNO-CASPT2 recovers more than 95% of the full CD-CASPT2 correlation energy while requiring only a fraction of the total virtual space, especially when large atomic orbital basis sets are in use. Tests on various properties commonly investigated with CASPT2 demonstrate the reliability of the approach and the associated reduction in computational cost and storage demand of the calculations.

We compute noncovalent intermolecular interaction energies for the S22 test set [Phys. Chem. Chem. Phys. 2006, 8, 1985-1993] of molecules at the Moller-Plesset and coupled cluster levels of supermolecular theory using density fitting (DF) to approximate all two-electron integrals. The error due to the DF approximation is analyzed for a range of auxiliary basis sets derived from Cholesky decomposition (CD) in conjunction with correlation consistent and atomic natural orbital valence basis sets. A Cholesky decomposition threshold of 10(-4)E(h) for full molecular CD and its one-center approximation (1C-CD) generally yields errors below 0.03 kcal/mol, whereas 10(-3)E(h) is sufficient to obtain the same level of accuracy or better with the atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets. Comparing to commonly used predefined auxiliary basis sets, we find that while the aCD and acCD sets are larger by a factor of 2-4 with triple-zeta AO basis sets, they provide results 1-2 orders of magnitude more accurate.

An algorithm for computing analytical gradients of the second-order Møller–Plesset (MP2) energy using density fitting (DF) is presented. The algorithm assumes that the underlying canonical Hartree–Fock reference is obtained with the same auxiliary basis set, which we obtain by Cholesky decomposition (CD) of atomic electron repulsion integrals. CD is also used for the negative semidefinite MP2 amplitude matrix. Test calculations on the weakly interacting dimers of the S22 test set (Jurečka et al., Phys. Chem. Chem. Phys. 2006, 8, 1985) show that the geometry errors due to the auxiliary basis set are negligible. With double-zeta basis sets, the error due to the DF approximation in intermolecular bond lengths is better than 0.1 pm. The computational time is typically reduced by a factor of 6–7.

Highly accurate estimates of the high-spin/low-spin energy, difference Delta E-HL(el) in the high-spin complexes [Fe(NCH)(6)](2+) and [Co(NCH)(6)](2+) have been obtained from the results of CCSD(T) calculations extrapolated to the complete basis set limit. These estimates are shown to be strongly influenced by scalar relativistic effects. They have been used to assess the performances of the CASPT2 method and 30 density functionals of the GGA, meta-GGA, global hybrid, RSH, and double-hybrid types. For the CASPT2 method, the results of the assessment support the proposal [Kepenekian, M.; Robert, V.; Le Guennic, B. J. Chem. Phys. 2009, 131, 114702] that the ionization potential-electron affinity (IPEA) shift defining the zeroth-order Hamiltonian be raised from its standard value of 0.25 au to 0.50-0.70 au for the determination of Delta E-HL(el) in Fe(II) complexes with a [FeN6] core. At the DFT level, some of the assessed functionals proved to perform within chemical accuracy (+/- 350 cm(-1)) for the spin-state energetics of [Fe(NCH)(6)](2+), others for that of [Co(NCH)(6)](2+), but none of them simultaneously for both complexes. As demonstrated through a reparametrization of the CAM-PBEO range-separated hybrid, which led to a functional that performs within chemical accuracy for the spin-state energetics of both complexes, performing density functionals of broad applicability may be devised by including in their training sets highly accurate data like those reported here for [Fe(NCH)(6)](2+) and [Co(NCH)(6)](2+).

We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 angstrom at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e. g., 0.032 angstrom with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 angstrom for S-0 and 0.11 angstrom for T-1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry. (C) 2014 AIP Publishing LLC.

We present a new approach for the calculation of dynamicelectron correlation effects in large molecular systems usingmulticonfigurational second-order perturbation theory(CASPT2). The method is restricted to cases where partitioningof the molecular system into an active site and an environment is meaningful. Only dynamic correlation effects derivedfrom orbitals extending over the active site are included at theCASPT2 level of theory, whereas the correlation effects of theenvironment are retrieved at lower computational costs. Forsufficiently large systems, the small errors introduced by thisapproximation are contrasted by the substantial savings inboth storage and computational demands compared to thefull CASPT2 calculation. Provided that static correlation effectsare correctly taken into account for the whole system, the proposed scheme represent a hierarchical approach to the electron correlation problem, where two molecular scales aretreated each by means of the most suitable level of theory.

A mechanism for the oxygenation of Cu-I complexes with alpha-keto-carboxylate 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 center dot(-) 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.

Multiconfigurational second-order perturbation theory calculations based on a complete active space reference wave function (CASPT2), employing active spaces of increasing size, are well converged at the level of 12 electrons in 12 orbitals for the singlet-triplet state-energy splittings of three supported copper-dioxygen and two supported copper-oxo complexes. Corresponding calculations using the restricted active space approach (RASPT2) offer similar accuracy with a significantly reduced computational overhead provided an inner (2,2) complete active space is included in the overall RAS space in order to account for strong biradical character in most of the compounds. The effects of the different active space choices and the outer RAS space excitations are examined, and conclusions are drawn with respect to the general applicability of the RASPT2 protocol.

Since the discovery of a formal quintuple bond in Ar’CrCrAr’ (CrCr = 1.835 angstrom) by Power and co-workers in 2005, many efforts have been dedicated to isolating dichromium species featuring quintuple-bond character. In the present study we investigate the electronic configuration of several, recently synthesized dichromium species with ligands using nitrogen to coordinate the metal centers. The bimetallic bond distances of Power’s compound and Cr-2-diazadiene (1) (CrCr = 1.803 angstrom) are compared to those found for Cr-2(mu-eta(2)-ArNC(R)NAr)(2) (2) (CrCr = 1.746 angstrom; R = H, Ar = 2,6-Et2C6H3), Cr-2(mu-eta(2)-(ArNC)-N-Xyl(H)NArXyl)(3) (3) (CrCr = 1.740(reduced)/1.817(neutral) angstrom; Ar-Xyl=2,6-C6H3-(CH3)(2)), Cr-2(mu-eta(2)-TippPyNMes)(2) (4) (CrCr = 1.749 angstrom; TippPyNMes = 6-(2,4,6-triisopropylphenyl)pyridin-2-yl (2,4,6-trimethylphenyl)-amide), and Cr-2(mu-eta(2)-DippNC(NMe2)N-Dipp)(2) (5) (CrCr = 1.729 angstrom, Dipp = 2,6-i-Pr2C6H3). We show that the correlation between the CrCr bond length and the effective bond order (EBO) is strongly affected by the nature of the ligand, as well as by the steric hindrance due to the ligand structure (e.g., the nature of the coordinating nitrogen). A linear correlation between the EBO and CrCr bond distance is established within the same group of ligands. As a result, the CrCr species based on the amidinate, aminopyridinate, and guanidinate ligands have bond patterns similar to the Ar’CrCrAr’ compound. Unlike these latter species, the dichromium diazadiene complex is characterized by a different bonding pattern involving Cr-N pi interactions, resulting in a lower bond order associated with the short metal-metal bond distance. In this case the short CrCr distance is most probably the result of the constraints imposed by the diazadiene ligand, implying a Cr2N4 core with a closer CrCr interaction.

Multiconfigurational quantum chemical calculations on the R-diimines dichromium compound confirm that the Cr-Cr bond, 1.80 angstrom, is among the shortest Cr-I-Cr-I bonds. However, the bond between the two Cr atoms is only a quadruple bond rather than a quintuple bond. The reason why the bond is so short has to be attributed to the strain in the NCCN ligand moieties.

A new multiconfigurational quantum chemical method, SplitGAS, is presented. The configuration interaction expansion, generated from a generalized active space, GAS, wave function is split in two parts, a principal part containing the most relevant configurations and an extended part containing less relevant, but not negligible, configurations. The partition is based on an orbital criterion. The SplitGAS method has been employed to study the HF, N-2, and Cr-2 molecules. The results on these systems, especially on the challenging, multiconfigurational Cr-2 molecule, are satisfactory. While SplitGAS is comparable with the GASSCF method in terms of memory requirements, it performs better than the complete active space method followed by second-order perturbation theory, CASPT2, in terms of equilibrium bond length, dissociation energy, and vibrational properties.

An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolution-of-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all HartreeFock and KohnSham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. 

Rooted in the very fundamental aspects of many chemical phenomena, and for the majority of photochemistry, is the onset of strongly interacting electronic configurations. To describe this challenging regime of strong electron correlation, an extraordinary effort has been put forward by a young generation of scientists in the development of theories 'beyond' standard wave function and density functional models. Despite their encouraging results, a twenty-and-more-year old approach still stands as the gold standard for these problems: multiconfiguration second-order perturbation theory based on complete active space reference wave function (CASSCF/CASPT2). We will present here a brief overview of the CASSCF/CASPT2 computational protocol, and of its role in our understanding of chemical and photochemical processes.

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 Mn2+ and Mn3+ oxidation states and accomplishes its enzymatic action in two half-cycles (corresponding to the oxidation and reduction of O-2(center dot-)). 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(center dot-) 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(center dot-) to H2O2 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 similar to 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) approximate to 10(4)-10(5) s(-1)).

We have developed a method to estimate accurate interaction energies between a full protein and a bound ligand. It is based oil 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 angstrom). 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%.

Results from a simulation of p-benzoquinone (PBQ) in water is presented. An explicit solvent representation is used together with a multiconfigurational ab initio quantum chemical method. The electronic n -> pi* transitions are studied in aqueous solution and the two such transitions are both blue-shifted but to different degree. Both non-equilibrium and many-body effects are found to have decisive influence on the solvation: despite stronger hydrogen bonding between solute and solvent in an excited state than in the ground state, there is a blue-shift, and the solvent structure around the non-polar PBQ is asymmetric, which is argued to come from special many-body effects. The unusual result of strengthened hydrogen bonds in the excited state that follows from an excitation of a non-bonding electron on a proton acceptor, is explained by the near-linear Stark shift that is present in the transition.