Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). II. The full rank NEVPT2 (FR-NEVPT2) formulation

In Paper I, the performances of pre-screening (PS), extended PS (EPS), and cumulant (CU) approximations to the fourth-order density matrix were examined in the context of second-order N-electron valence state perturbation theory (NEVPT2). It has been found that the CU, PS, and even EPS approximations with loose thresholds may introduce intruder states. In the present work, the origin of these “false intruder” states introduced by approximated density matrices is discussed. Canonical NEVPT2 implementations employ a rank reduction trick. By analyzing its residual error, we find that the omission of the rank reduction leads to a more stable multireference perturbation theory for incomplete active space reference wave functions. Such a full rank (FR)-NEVPT2 formulation is equivalent to the conventional NEVPT2 method for the complete active space self-consistent field/complete active space configuration interaction reference wave function. A major drawback of the FR-NEVPT2 formulation is the necessity of the fifth-order density matrix. To avoid the construction of the high-order density matrices, the combination of the FR-NEVPT2 with the CU approximation is studied. However, we find that the CU approximation remains problematic as it still introduces intruder states. The question of how to robustly and efficiently perform internally contracted multireference perturbation theories with approximate densities remains a challenging field of investigation

An efficient implementation of the NEVPT2 and CASPT2 methods avoiding higher-order density matrices

A factorization of the matrix elements of the Dyall Hamiltonian in N-electron valence state perturbation theory allowing their evaluation with a computational effort comparable to the one needed for the construction of the third-order reduced density matrix at the most is presented. Thus, the computational bottleneck arising from explicit evaluation of the fourth-order density matrix is avoided. It is also shown that the residual terms arising in the case of an approximate complete active space configuration interaction solution and containing even the fifth-order density matrix for two excitation classes can be evaluated with little additional effort by choosing again a favorable factorization of the corresponding matrix elements. An analogous argument is also provided for avoiding the fourth-order density matrix in complete active space second-order perturbation theory. Practical calculations indicate that such an approach leads to a considerable gain in computational efficiency without any compromise in numerical accuracy or stability

Converged Structural and Spectroscopic Properties for Refined QM/MM Models of Azurin

Blue copper proteins continue to challenge experiment and theory with their electronic structure and spectroscopic properties that respond sensitively to the coordination environment of the copper ion. In this work, we report state-of-the art electronic structure studies for geometric and spectroscopic properties of the archetypal “Type I” copper protein azurin in its Cu(II) state. A hybrid quantum mechanics/molecular mechanics (QM/MM) approach is used, employing both density functional theory (DFT) and coupled cluster with singles, doubles, and perturbative triples (CCSD(T)) methods for the QM region, the latter method making use of the domain-based local pair natural orbital (DLPNO) approach. Models of increasing QM size are employed to investigate the convergence of critical geometric parameters. It is shown that convergence is slow and that a large QM region is critical for reproducing the short experimental Cu–SCys112 distance. The study of structural convergence is followed by investigation of spectroscopic parameters using both DFT and DLPNO-CC methods and comparing these to the experimental spectrum using simulations. The results allow us to examine for the first time the distribution of spin densities and hyperfine coupling constants at the coupled cluster level, leading us to revisit the experimental assignment of the 33S hyperfine splitting. The wavefunction-based approach to obtain spin-dependent properties of open-shell systems demonstrated here for the case of azurin is transferable and applicable to a large array of bioinorganic systems

Outer-Sphere Contributions to the Electronic Structure of Type Zero Copper Proteins

Bioinorganic canon states that active-site thiolate coordination promotes rapid electron transfer (ET) to and from type 1 copper proteins. In recent work, we have found that copper ET sites in proteins also can be constructed without thiolate ligation (called “type zero” sites). Here we report multifrequency electron paramagnetic resonance (EPR), magnetic circular dichroism (MCD), and nuclear magnetic resonance (NMR) spectroscopic data together with density functional theory (DFT) and spectroscopy-oriented configuration interaction (SORCI) calculations for type zero Pseudomonas aeruginosa azurin variants. Wild-type (type 1) and type zero copper centers experience virtually identical ligand fields. Moreover, O-donor covalency is enhanced in type zero centers relative that in the C112D (type 2) protein. At the same time, N-donor covalency is reduced in a similar fashion to type 1 centers. QM/MM and SORCI calculations show that the electronic structures of type zero and type 2 are intimately linked to the orientation and coordination mode of the carboxylate ligand, which in turn is influenced by outer-sphere hydrogen bonding

Structure–Spectroscopy Correlations for Intermediate Q of Soluble Methane Monooxygenase: Insights from QM/MM Calculations

The determination of the diiron core intermediate structures involved in the catalytic cycle of soluble methane monooxygenase (sMMO), the enzyme that selectively catalyzes the conversion of methane to methanol, has been a subject of intense interest within the bioinorganic scientific community. Particularly, the specific geometry and electronic structure of the intermediate that precedes methane binding, known as intermediate Q (or MMOHQ), has been debated for over 30 years. Some reported studies support a bis-μ-oxo-bridged Fe(IV)2O2 closed-core conformation Fe(IV)2O2 core, whereas others favor an open-core geometry, with a longer Fe–Fe distance. The lack of consensus calls for a thorough re-examination and reinterpretation of the spectroscopic data available on the MMOHQ intermediate. Herein, we report extensive simulations based on a hybrid quantum mechanics/molecular mechanics approach (QM/MM) approach that takes into account the complete enzyme to explore possible conformations for intermediates MMOHox and MMOHQ of the sMMOH catalytic cycle. High-level quantum chemical approaches are used to correlate specific structural motifs with geometric parameters for comparison with crystallographic and EXAFS data, as well as with spectroscopic data from Mössbauer spectroscopy, Fe K-edge high-energy resolution X-ray absorption spectroscopy (HERFD XAS), and resonance Raman 16O–18O difference spectroscopy. The results provide strong support for an open-core-type configuration in MMOHQ, with the most likely topology involving mono-oxo-bridged Fe ions and alternate terminal Fe-oxo and Fe-hydroxo groups that interact via intramolecular hydrogen bonding. The implications of an open-core intermediate Q on the reaction mechanism of sMMO are discussed

Cobalt-Catalyzed Hydrosilylation of Carbon Dioxide to the Formic Acid, Formaldehyde, and Methanol Level—How to Control the Catalytic Network?

The selective hydrosilylation of carbon dioxide (CO2) to either the formic acid, formaldehyde, or methanol level using a molecular cobalt(II) triazine complex can be controlled based on reaction parameters such as temperature, CO2 pressure, and concentration. Here, we rationalize the catalytic mechanism that enables the selective arrival at each product platform. Key reactive intermediates were prepared and spectroscopically characterized, while the catalytic mechanism and the energy profile were analyzed with density functional theory (DFT) methods and microkinetic modeling. It transpired that the stepwise reduction of CO2 involves three consecutive catalytic cycles, including the same cobalt(I) triazine hydride complex as the active species. The increasing kinetic barriers associated with each reduction step and the competing hydride transfer steps in the three cycles corroborate the strong influence of the catalyst environment on the product selectivity. The fundamental mechanistic insights provide a consistent description of the catalytic system and rationalize, in particular, the experimentally verified opportunity to steer the reaction toward the formaldehyde product as the chemically most challenging reduction level

Di- and Trinuclear Mixed-Valence Copper Amidinate Complexes from Reduction of Iodine

Molecular examples of mixed-valence copper complexes through chemical oxidation are rare but invoked in the mechanism of substrate activation, especially oxygen, in copper-containing enzymes. To examine the cooperative chemistry between two metals in close proximity to each other we began studying the reactivity of a dinuclear Cu(I) amidinate complex. The reaction of [(2,6-Me2C6H3N)2C(H)]2Cu2, 1, with I2 in tetrahydrofuran (THF), CH3CN, and toluene affords three new mixed-valence copper complexes [(2,6-Me2C6H3N)2C(H)]2Cu2(μ2-I3)(THF)2, 2, [(2,6-Me2C6H3N)2C(H)]2Cu2(μ2-I) (NCMe)2, 3, and [(2,6-Me2C6H3N)2C(H)]3Cu3(μ3-I)2, 4, respectively. The first two compounds were characterized by UV-vis and electron paramagnetic resonance spectroscopies, and their molecular structure was determined by X-ray crystallography. Both di- and trinuclear mixed-valence intermediates were characterized for the reaction of compound 1 to compound 4, and the molecular structure of 4 was determined by X-ray crystallography. The electronic structure of each of these complexes was also investigated using density functional theory

Laboratory Characterization and Astrophysical Detection of Vibrationally Excited States of Vinyl Cyanide in Orion-KL

New laboratory data of CH$_2$CHCN (vinyl cyanide) in its ground and vibrationally excited states at the microwave to THz domain allow searching for these excited state transitions in the Orion-KL line survey. Frequency-modulated spectrometers combined into a single broadband 50-1900 GHz spectrum provided measurements of CH$_2$CHCN covering a spectral range of 18-1893 GHz, whose assignments was confirmed by Stark modulation spectra in the 18-40 GHz region and by ab-initio anharmonic force field calculations. For analyzing the emission lines of CH$_2$CHCN species detected in Orion-KL we used the excitation and radiative transfer code (MADEX) at LTE conditions. The rotational transitions of the ground state of this molecule emerge from four cloud components of hot core nature which trace the physical and chemical conditions of high mass star forming regions in the Orion-KL Nebula. The total column density of CH$_2$CHCN in the ground state is (3.0$\pm$0.9)x10$^{15}$ cm$^{-2}$. We report on the first interstellar detection of transitions in the v10=1/(v11=1,v15=1) dyad in space, and in the v11=2 and v11=3 states in Orion-KL. The lowest energy vibrationally excited states of vinyl cyanide such as v11=1 (at 328.5 K), v15=1 (at 478.6 K), v11=2 (at 657.8 K), the v10=1/(v11=1,v15=1) dyad (at 806.4/809.9 K), and v11=3 (at 987.9 K) are populated under warm and dense conditions, so they probe the hottest parts of the Orion-KL source. Column density and rotational and vibrational temperatures for CH$_2$CHCN in their ground and excited states, as well as for the isotopologues, have been constrained by means of a sample of more than 1000 lines in this survey. Moreover, we present the detection of methyl isocyanide (CH$_3$NC) for the first time in Orion-KL and a tentative detection of vinyl isocyanide (CH$_2$CHNC) and give column density ratios between the cyanide and isocyanide isomers.Comment: 46 pages, 22 figures, 14 tables, 9 online table