Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry

We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently developed hierarchical tensor representations, in particular tensor trains which are matrix product states in physics language. The discrete equations of full CI approximation applied to the electronic Schr\"odinger equation is casted into a tensorial framework in form of the second quantization. A further approximation is performed afterwards by tensor approximation within a hierarchical format or equivalently a tree tensor network. We establish the (differential) geometry of low rank hierarchical tensors and apply the Driac Frenkel principle to reduce the original high-dimensional problem to low dimensions. The DMRG algorithm is established as an optimization method in this format with alternating directional search. We briefly introduce the CC method and refer to our theoretical results. We compare this approach in the present discrete formulation with the CC method and its underlying exponential parametrization.Comment: 15 pages, 3 figure

Stepwise basis set selection

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146410/1/jcc25363.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146410/2/jcc25363_am.pd

Systematic investigation of the influence of electronic substituents on dinuclear gold( i ) amidinates: synthesis, characterisation and photoluminescence studies

Dinuclear gold(I) compounds are of great interest due to their aurophilic interactions that influence their photophysical properties. Herein, we showcase that gold–gold interactions can be influenced by tuning the electronic properties of the ligands. Therefore, various para substituted (R) N,N′-bis(2,6-dimethylphenyl)formamidinate ligands (pRXylForm; Xyl = 2,6-dimethylphenyl and Form = formamidinate) were treated with Au(tht)Cl (tht = tetrahydrothiophene) to give via salt metathesis the corresponding gold(I) compounds [pRXylForm$_2$Au$_2$] (R = –OMe, –Me, –Ph, –H, –SMe, and –CO$_2$Me). All complexes showed intense luminescence properties at low temperatures. Alignment with the Hammett parameter σ$_p$ revealed the trends in the $^1$H and $^{13}$C NMR spectra. These results showed the influence of the donor–acceptor abilities of different substituents on the ligand system which were confirmed with calculated orbital energies. Photophysical investigations showed their lifetimes in the millisecond range indicating phosphorescence processes and revealed a redshift with the decreasing donor ability of the substituents in the solid state

Cooperativity in luminescent heterobimetallic diphosphine-β-diketiminate complexes

The bis(phosphine)-functionalized β-diketiminate ligand [HC{(CH$_3$)C}$_2${(o-[P(C$_6$H$_5$)$_2$]$_2$C$_6$H$_4$)N}$_2$]$^−$(PNac) was used for the synthesis of luminescent closed-shell bimetallic complexes. The PNNP pocket combining both soft and hard donor sites can act as an orthogonal ligand scaffold to selectively coordinate two different metal ions. Deprotonation and subsequent salt elimination with [AuCl(tht)] (tht = tetrahydrothiophene) or AgI yielded the mononuclear complexes [PNacAu] (1) or [PNacAg] (2), respectively. The AuI ion is linearly coordinated by the two phosphines, forming a 12-membered metalla-macrocycle with an empty β-diketiminate pocket available for complexation of hard d$^{10}$ metal ions (Zn$^{II}$, Cd$^{II}$, and Hg$^{II}$). According to this synthetic protocol, a series of heterobimetallic complexes were isolated. The complexation of the second metal ion in close spatial proximity has led to drastic changes in the photophysical properties. For further studies and understanding, quantum chemical calculations were performed

Bi- and trinuclear coinage metal complexes of a PNNP ligand featuring metallophilic interactions and an unusual charge separation

A selective synthesis of bi- and trinuclear complexes featuring a tetradentate monoanionic PNNP ligand is presented. The binuclear coinage metal complexes show a typical fourfold coordination for Cu and Ag, which changes to a bifold coordination for Au. The latter is accompanied by an unusual charge separation. Optical properties are investigated using photoluminescence spectroscopy and complemented by time-dependent density-functional-theory calculations. All compounds demonstrate clearly distinguished features dependent on the metals chosen and differences in the complex scaffold

Investigation of the Coordination Chemistry of a Bisamidinate Ferrocene Ligand with Cu, Ag, and Au

The coordination chemistry of a ferrocene ligand with one bulky amidinate function attached to each ring toward two different coinage metal precursors was investigated. In dependence of the metal and the co-ligands, “ansa” type structures and non-bridged structures were obtained. Six different compounds are reported. In the “ansa” type structures, short Fe–M (M = Cu, Ag) distances were observed in the molecular structures in the solid state. However, theoretical calculations (DFT) did not reveal a stabilizing metal–metal interaction. Instead, dispersion interactions within the ligand and between the ligand and metal seem to represent the main stabilization forces

Bright Luminescence in Three Phases—A Combined Synthetic, Spectroscopic and Theoretical Approach

Combining phase-dependent photoluminescence (PL) measurements and quantum chemical calculations is a powerful approach to help understand the influence of the molecular surroundings on the PL properties. Herein, a phosphine functionalized amidinate was used to synthesize a recently presented bimetallic gold complex, featuring an unusual charge separation. The latter was subsequently used as metalloligand to yield heterotetrametallic complexes with an Au-M-M-Au “molecular wire” arrangement (M=Cu, Ag, Au) featuring metallophilic interactions. All compounds show bright phosphorescence in the solid state, also at ambient temperature. The effect of the molecular environment on the PL was studied in detail for these tetrametallic complexes by comparative measurements in solution, in the solid state and in the gas phase and contrasted to time-dependent density functional theory computations

Scattering length of the ground state Mg+Mg collision

We have constructed the X 1SIGMAg+ potential for the collision between two ground state Mg atoms and analyzed the effect of uncertainties in the shape of the potential on scattering properties at ultra-cold temperatures. This potential reproduces the experimental term values to 0.2 inverse cm and has a scattering length of +1.4(5) nm where the error is prodominantly due to the uncertainty in the dissociation energy and the C6 dispersion coefficient. A positive sign of the scattering length suggests that a Bose-Einstein condensate of ground state Mg atoms is stable.Comment: 15 pages, 3 figures, Submitted Phys. Rev.