Decomposition of density matrix renormalization group states into a Slater determinant basis

The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants.     

Theoretical transition probabilities for the OH Meinel system

The authors present a new potential energy curve, electric dipole moment function, and spin-orbit coupling function for OH in the X 2Pi state, based on high-level ab initio calculations. These properties, combined with a spectroscopically parametrized lambda-type doubling Hamiltonian, are used to compute the Einstein A coefficients and photoabsorption cross sections for the OH Meinel transitions. The authors investigate the effect of spin-orbit coupling on the lifetimes of rovibrationally excited states. Comparing their results with earlier ab initio calculations, they conclude that their dipole moment and potential energy curve give the best agreement with experimental data to date. The results are made available via EPAPS Document No. E-JCPSAG-017709.     

Ab initio calculation of the NH(3sigma-)-NH(3sigma-) interaction potentials in the quintet, triplet, and singlet states

We present the ab initio potential-energy surfaces of the NH-NH complex that correlate with two NH molecules in their 3sigma- electronic ground state. Three distinct potential-energy surfaces, split by exchange interactions, correspond to the coupling of the S(A) = 1 and S(B) = 1 electronic spins of the monomers to dimer states with S = 0, 1, and 2. Exploratory calculations on the quintet (S = 2), triplet (S = 1), and singlet (S = 0) states and their exchange splittings were performed with the valence bond self-consistent-field method that explicitly accounts for the nonorthogonality of the orbitals on different monomers. The potential surface of the quintet state, which can be described by a single Slater determinant reference function, was calculated at the coupled cluster level with single and double excitations and noniterative treatment of the triples. The triplet and singlet states require multiconfiguration reference wave functions and the exchange splittings between the three potential surfaces were calculated with the complete active space self-consistent-field method supplemented with perturbative configuration interaction calculations of second and third orders. Full potential-energy surfaces were computed as a function of the four intermolecular Jacobi coordinates, with an aug-cc-pVTZ basis on the N and H atoms and bond functions at the midpoint of the intermolecular vector R. An analytical representation of these potentials was given by expanding their dependence on the molecular orientations in coupled spherical harmonics, and representing the dependence of the expansion coefficients on the intermolecular distance R by the reproducing kernel Hilbert space method. The quintet surface has a van der Waals minimum of depth D(e) = 675 cm(-1) at R(e) = 6.6a0 for a linear geometry with the two NH electric dipoles aligned. The singlet and triplet surfaces show similar, slightly deeper, van der Waals wells, but when R is decreased the weakly bound NH dimer with S = 0 and S = 1 converts into the chemically bound N2H2 diimide (also called diazene) molecule with only a small energy barrier to overcome.     

Efficient Blue‐Colored Solid‐State Dye‐Sensitized Solar Cells: Enhanced Charge Collection by Using an in Situ Photoelectrochemically Generated Conducting Polymer Hole Conductor

A high power conversion efficiency (PCE) of 5.5 % was achieved by efficiently incorporating a diketopyrrolopyrrole‐based dye with a conducting polymer poly(3,4‐ethylenediothiophene) (PEDOT) hole‐transporting material (HTM) that was formed in situ, compared with a PCE of 2.9 % for small molecular spiro‐OMeTAD‐based solid‐state dye solar cells (sDSCs). The high PCE for PEDOT‐based sDSCs is mainly attributed to the significantly enhanced charge‐collection efficiency, as a result of the three‐order‐of‐magnitude higher hole conductivity (0.53 S cm^?1) compared with that of the widely used low molecular weight HTM spiro‐OMeTAD (3.5×10^?4 S cm^?1).     

Analysis of spin states, spin barriers, and trans-effects involved in the coordination and stabilization of dinitrogen by biomimetic iron complexes

Coordination of dinitrogen to Sellmann-type iron (II) complexes in a sulfur-dominated coordination sphere, which emulates the environment of iron centers in the FeMo-cofactor of nitrogenase, is analyzed with respect to spin states, spin barriers, and the effect of trans-ligands. Such detailed investigations became only recently feasible when the reliability of density functional methods, which are the only quantum chemical methods capable of describing large transition metal complexes, could significantly be improved for the calculation of energies for states of different spin. It is found that the actual binding energy of dinitrogen is of sufficient magnitude for a reasonably strong fixation of N₂ by Sellmann-type coordination compounds. However, potential fixation is determined by additional factors which reduce the binding energy. One factor is the change in spin state of the N₂-free metal fragment, which lowers the total energy and quenches the thermodynamic stabilization effect of the binding energy. In addition, the metal fragment rearranges and gains even more stabilization energy for the un-coordinated state. Apart from these thermodynamical effects, the existence of spin barriers, which must be overcome upon binding of dinitrogen, leads to kinetical effects, which cannot be neglected.     

Determination of the light-induced degradation rate of the solar cell sensitizer N719 on TiO2 nanocrystalline particles

The oxidative degradation rate, kdeg, of the solar cell dye (Bu4N+)2[Ru(dcbpyH)2(NCS)2]2-, referred to as N719 or [RuL2(NCS)2], was obtained by applying a simple model system. Colloidal solutions of N719-dyed TiO2 particles in acetonitrile were irradiated with 532-nm monochromatic light, and the sum of the quantum yields for the oxidative degradation products [RuL2(CN)2], [RuL2(NCS)(CN)], and [RuL2(NCS)(ACN)], Phideg, was obtained at eight different light intensities in the range of 0.1-16.30 mW/cm2 by LC-UV-MS. The Phideg values decreased from 3.3 x 10-3 to 2.0 x 10-4 in the applied intensity range. By using the relation kdeg = Phidegkback and back electron-transfer reaction rates, kback, obtained with photoinduced absorption spectroscopy, it was possible to calculate an average value for the oxidative degradation rate of N719 dye attached to TiO2 particles, kdeg = 4.0 x 10-2 s-1. The stability of N719 dye during solar cell operation was discussed based on this number, and on values of the electron-transfer rate between [Ru(III)L2(NCS)2] and iodide ion that are available in the literature.     

Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings

The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.     

4-Phosphoryl Pyrazolones for Highly Selective Lithium Separation from Alkali Metal Ions

Effective receptors for the separation of Li⁺ from a mixture with other alkali metal ions under mild conditions remains an important challenge that could benefit from new approaches. In this study, it is demonstrated that the 4-phosphoryl pyrazolones, H L ²-H L ⁴, in the presence of the typical industrial organophosphorus co-ligands tributylphosphine oxide (TBPO), tributylphosphate (TBP) and trioctylphosphine oxide (TOPO), are able to selectively recognise and extract lithium ions from aqueous solution. Structural investigations in solution as well as in the solid state reveal the existence of a series of multinuclear Li⁺ complexes that include dimers (TBPO, TBP) as well as rarely observed trimers (TOPO) and represent the first clear evidence for the synergistic role of the co-ligands in the extraction process. Our findings are supported by detailed NMR, MS and extraction studies. Liquid-liquid extraction in the presence of TOPO revealed an unprecedented high Li⁺ extraction efficiency (78 %) for H L ⁴ compared to the use of the industrially employed acylpyrazolone H L ¹ (15 %) and benzoyl-1,1,1-trifluoroacetone (52 %) extractants. In addition, a high selectivity for Li⁺ over Na⁺, K⁺ and Cs⁺ under mild conditions (pH ∼8.2) confirms that H L ²-H L ⁴ represent a new class of ligands that are very effective extractants for use in lithium separation.