Efficient calculation of Franck–Condon factors and vibronic couplings in polyatomics

We present a technique for the calculation of Franck–Condon factors and other integrals between vibronic wave functions belonging to different electronic states. The technique is well suited for the determination of the nonadiabatic or spin‐orbit couplings related to radiationless decays in polyatomics. Rigorous or approximate partitions of the internal coordinate space are exploited to achieve better efficiency and/or to go beyond the harmonic approximation. The technique is tested by computing the Internal Conversion and InterSystem Crossing rates of (CH₃)₃CNO in its ¹(n→π*) state. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 968–975, 2001     

Simple evaluation of Franck–Condon factors and non‐Condon effects in the Morse potential

The calculation of Franck–Condon factors between different 1‐D Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a simple program written in Mathematica are compared with other calculations. We show that our results have a similar accuracy as those calculations performed with more sophisticated methods. We discuss the extension of our method to include non‐Condon effects in the calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 280–295, 2002     

Potential‐Energy Surfaces,the Born–Oppenheimer Approximations,and the Franck–Condon Principle: Back to the Roots

The concept of a potential‐energy surface (PES) is central to our understanding of spectroscopy, photochemistry, and chemical kinetics. However, the terminology used in connection with the basic approximations is variously, and somewhat confusingly, represented with such phrases as “adiabatic”, “Born–Oppenheimer”, or “Born–Oppenheimer adiabatic” approximation. Concerning the closely relevant and important Franck–Condon principle (FCP), the IUPAC definition differentiates between a classical and quantum mechanical formulation. Consequently, in many publications we find terms such as “Franck–Condon (excited) state”, or a vertical transition to the “Franck–Condon point” with the “Franck–Condon geometry” that relaxes to the excited‐state equilibrium geometry. The Born–Oppenheimer approximation and the “classical” model of the Franck–Condon principle are typical examples of misused terms and lax interpretations of the original theories. In this essay, we revisit the original publications of pioneers of the PES concept and the FCP to help stimulate a lively discussion and clearer thinking around these important concepts.     

The convolution theorem and the Franck–Condon integral

The convolution theorem is used to evaluate the Franck–Condon integral. It is shown that this integral becomes the matrix element between two “squeezed” states. This enables one to evaluate the integral by using boson operators. In addition, a general method is developed to obtain integrals involving Hermite polynomials with a displaced argument. In particular, the two‐center matrix element _g〈m|f(x_e)|n〉_e, is obtained, where f(x_e)=exp(Dx+Fx_e). ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 11–15, 1999     

Franck–Condon simulation of photoelectron spectroscopy of HOO: Including Duschinsky effects

Geometry optimization and harmonic vibrational frequency calculations were performed on the and states of HOO and state of HOO⁻. The electron affinity and the term energy () of HOO were calculated at various theory levels. Franck–Condon analyses and spectral simulations were carried out on the and photodetachment processes. The spectral simulations of vibrational structures based on the computed Franck–Condon factors are in excellent agreement with the observed spectra. In addition, the equilibrium geometrical parameters of the state of HOO⁻ and state of HOO were obtained in the spectral simulations.     

Franck–Condon factors for the Morse potential

The aim of this study is to establish a new representation for the dynamic algebra of the Morse oscillator and to establish the raising and lowering operators based on the properties of the confluent hypergeometric functions. Using the representation we have obtained a recurrent analytic method for the calculus of the Franck–Condon factors. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 655–660, 1997     

Unified analytical treatment for calculation of the two‐dimensional Franck–Condon factors using the duschinsky transformation

Including binomial expansion theorems, we present an analytical formula for calculating Franck–Condon (FC) factors of two‐dimensional (2D) harmonic oscillators including the Duschinsky effect. The FC principle has various practical applications in quantum modeling of electronic spectra of polyatomic molecules. The 2D FC factors are expressed through the binomial coefficients. Use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speeder calculation, should such limits be required in practice. Accurate numerical results are provided to validate the proposed algorithm. © 2012 Wiley Periodicals, Inc.     

A Boiling‐Water‐Stable,Tunable White‐Emitting Metal–Organic Framework from Soft‐Imprint Synthesis

A new avenue for making porous frameworks has been developed by borrowing an idea from molecularly imprinted polymers (MIPs). In lieu of the small molecules commonly used as templates in MIPs, soft metal components, such as CuI, are used to orient the molecular linker and to leverage the formation of the network. Specifically, a linear dicarboxylate linker with thioether side groups reacted simultaneously with Ln³⁺ ions and CuI, leading to a bimetallic net featuring strong, chemically hard Eu³⁺–carboxylate links, as well as soft, thioether‐bound Cu₂I₂ clusters. The CuI block imparts water stability to the host; with the tunable luminescence from the lanthanide ions, this creates the first white‐emitting MOF that is stable in boiling water. The Cu₂I₂ block also readily reacts with H₂S, and enables sensitive colorimetric detection while the host net remains intact.     

Defect‐Engineered Metal–Organic Frameworks

Defect engineering in metal–organic frameworks (MOFs) is an exciting concept for tailoring material properties, which opens up novel opportunities not only in sorption and catalysis, but also in controlling more challenging physical characteristics such as band gap as well as magnetic and electrical/conductive properties. It is challenging to structurally characterize the inherent or intentionally created defects of various types, and there have so far been few efforts to comprehensively discuss these issues. Based on selected reports spanning the last decades, this Review closes that gap by providing both a concise overview of defects in MOFs, or more broadly coordination network compounds (CNCs), including their classification and characterization, together with the (potential) applications of defective CNCs/MOFs. Moreover, we will highlight important aspects of “defect‐engineering” concepts applied for CNCs, also in comparison with relevant solid materials such as zeolites or COFs. Finally, we discuss the future potential of defect‐engineered CNCs.     

A Stable Microporous Mixed‐Metal Metal–Organic Framework with Highly Active Cu2+ Sites for Efficient Cross‐Dehydrogenative Coupling Reactions

Two metalloporphyrin octacarboxylates were used to link copper(II) nodes for the formation of two novel porous mixed‐metal metal–organic frameworks (M′MOFs) containing nanopore cages (2.1 nm in diameter) or nanotubular channels (1.5 nm in diameter). The highly active Cu²⁺ sites on the nanotubular surfaces of the stable porous M′MOF ZJU‐22 , stabilized by three‐connected nets, lead to the superior catalytic activity for the cross‐dehydrogenative coupling (CDC) reaction.     

Flexible and Hierarchical Metal–Organic Framework Composites for High‐Performance Catalysis

The development of porous composite materials is of great significance for their potentially improved performance over those of individual components and extensive applications in separation, energy storage, and heterogeneous catalysis. Now mesoporous metal–organic frameworks (MOFs) with macroporous melamine foam (MF) have been integrated using a one‐pot process, generating a series of MOF/MF composite materials with preserved crystallinity, hierarchical porosity, and increased stability over that of melamine foam. The MOF nanocrystals were threaded by the melamine foam networks, resembling a ball‐and‐stick model overall. The resulting MOF/MF composite materials were employed as an effective heterogeneous catalyst for the epoxidation of cholesteryl esters. Combining the advantages of interpenetrative mesoporous and macroporous structures, the MOF/melamine foam composite has higher dispersibility and more accessibility of catalytic sites, exhibiting excellent catalytic performance.     

Defect‐Controlled Preparation of UiO‐66 Metal–Organic Framework Thin Films with Molecular Sieving Capability

Metal–organic framework (MOF) UiO‐66 thin films are solvothermally grown on conducting substrates. The as‐synthesized MOF thin films are subsequently dried by a supercritical process or treated with polydimethylsiloxane (PDMS). The obtained UiO‐66 thin films show excellent molecular sieving capability as confirmed by the electrochemical studies for redox‐active species with different sizes.     

pH‐Dependent Proton Conducting Behavior in a Metal–Organic Framework Material

A porous metal–organic framework (MOF), [Ni₂(dobdc)(H₂O)₂]?6 H₂O (Ni₂(dobdc) or Ni‐MOF‐74; dobdc^4?=2,5‐dioxido‐1,4‐benzenedicarboxylate) with hexagonal channels was synthesized using a microwave‐assisted solvothermal reaction. Soaking Ni₂(dobdc) in sulfuric acid solutions at different pH values afforded new proton‐conducting frameworks, H⁺@Ni₂(dobdc). At pH 1.8, the acidified MOF shows proton conductivity of 2.2×10^?2 S cm^?1 at 80 °C and 95 % relative humidity (RH), approaching the highest values reported for MOFs. Proton conduction occurs via the Grotthuss mechanism with a significantly low activation energy as compared to other proton‐conducting MOFs. Protonated water clusters within the pores of H⁺@Ni₂(dobdc) play an important role in the conduction process.     

Self‐Assembly versus Stepwise Synthesis: Heterometal–Organic Frameworks Based on Metalloligands with Tunable Luminescence Properties

A new family of heterometal–organic frameworks has been prepared by two synthesis strategies, in which IFMC‐26 and IFMC‐27 are constructed by self‐assembly and IFMC‐28 is obtained by stepwise synthesis based on the metalloligand (IFMC=Institute of Functional Material Chemistry). IFMC‐26 is a (3,6)‐connected net and IFMC‐27 is a (4,8)‐connected 3D framework. The metalloligands {Ni(H₄L)}(NO₃)₂ are connected by binuclear lanthanide clusters giving rise to a 2D sheet structure in IFMC‐28 . Notably, IFMC‐26‐Eu _x Tb _y and IFMC‐28‐Eu _x Tb _y have been obtained by changing the molar ratios of raw materials. Owing to the porosity of IFMC‐26 , Tb³⁺@IFMC‐26‐Eu and Eu³⁺@IFMC‐26‐Tb are obtained by postencapsulating Tb^III and Eu^III ions into the pores, respectively. Tunable luminescence in metal–organic frameworks is achieved by the two kinds of doping methods. In particular, the quantum yields of heterometal–organic frameworks are apparently enhanced by postencapsulation of Ln^III ions.     

Chemical and Structural Stability of Zirconium‐based Metal–Organic Frameworks with Large Three‐Dimensional Pores by Linker Engineering

The synthesis of metal–organic frameworks with large three‐dimensional channels that are permanently porous and chemically stable offers new opportunities in areas such as catalysis and separation. Two linkers (L1=4,4′,4′′,4′′′‐([1,1′‐biphenyl]‐3,3′,5,5′‐tetrayltetrakis(ethyne‐2,1‐diyl)) tetrabenzoic acid, L2=4,4′,4′′,4′′′‐(pyrene‐1,3,6,8‐tetrayltetrakis(ethyne‐2,1‐diyl))tetrabenzoic acid) were used that have equivalent connectivity and dimensions but quite distinct torsional flexibility. With these, a solid solution material, [Zr₆O₄(OH)₄(L1)_2.6(L2)_0.4]?(solvent)_x, was formed that has three‐dimensional crystalline permanent porosity with a surface area of over 4000 m² g^?1 that persists after immersion in water. These properties are not accessible for the isostructural phases made from the separate single linkers.     

A Bismuth‐Based Metal–Organic Framework as an Efficient Visible‐Light‐Driven Photocatalyst

A visible‐light‐responsive bismuth‐based metal–organic framework (Bi‐mna) is demonstrated to show good photoelectric and photocatalytic properties. Combining experimental and theoretical results, a ligand‐to‐ligand charge transfer (LLCT) process is found to be responsible for the high performance, which gives rise to a longer lifetime of photogenerated charge carriers. Our results suggest that bismuth‐based MOFs could be promising candidates for the development of efficient visible‐light photocatalysts.     

The First One‐Pot Synthesis of Metal–Organic Frameworks Functionalised with Two Transition‐Metal Complexes

The synthesis of a metal–organic framework (UiO‐67) functionalised simultaneously with two different transition metal complexes (Ir and Pd or Rh) through a one‐pot procedure is reported for the first time. This has been achieved by an iterative modification of the synthesis parameters combined with characterisation of the resulting materials using different techniques, including X‐ray absorption spectroscopy (XAS). The method also allows the first synthesis of UiO‐67 with a very wide range of loadings (from 4 to 43 mol %) of an iridium complex ([IrCp*(bpydc)(Cl)Cl]^2?; bpydc=2,2′‐bipyridine‐5,5′‐dicarboxylate, Cp*=pentamethylcyclopentadienyl) through a pre‐functionalisation methodology.     

Symmetry‐Guided Synthesis of Highly Porous Metal–Organic Frameworks with Fluorite Topology

Two stable, non‐interpenetrated MOFs, PCN‐521 and PCN‐523, were synthesized by a symmetry‐guided strategy. Augmentation of the 4‐connected nodes in the fluorite structure with a rigid tetrahedral ligand and substitution of the 8‐connected nodes by the Zr/Hf clusters yielded MOFs with large octahedral interstitial cavities. They are the first examples of Zr/Hf MOFs with tetrahedral linkers. PCN‐521 has the largest BET surface area (3411 m² g^‐1), pore size (20.5×20.5×37.4 Å) and void volume (78.5%) of MOFs formed from tetrahedral ligands. This work not only demonstrates a successful implementation of rational design of MOFs with desired topology, but also provides a systematic way of constructing non‐interpenetrated MOFs with high porosity.     

Two‐in‐One: Inherent Anhydrous and Water‐Assisted High Proton Conduction in a 3D Metal–Organic Framework

The development of solid‐state proton‐conducting materials with high conductivity that operate under both anhydrous and humidified conditions is currently of great interest in fuel‐cell technology. A 3D metal–organic framework (MOF) with acid–base pairs in its coordination space that efficiently conducts protons under both anhydrous and humid conditions has now been developed. The anhydrous proton conductivity for this MOF is among the highest values that have been reported for MOF materials, whereas its water‐assisted proton conductivity is comparable to that of the organic polymer Nafion, which is currently used for practical applications. Unlike other MOFs, which conduct protons either under anhydrous or humid conditions, this compound should represent a considerable advance in the development of efficient solid‐state proton‐conducting materials that work under both anhydrous and humid conditions.