Distinguishing the Strength of Electronic Coupling for Mo2‐Containing Mixed‐Valence Compounds within the Class III Regime

Two, symmetrical, mixed‐valence (MV), complex cations—{[Mo₂(DAniF)₃]₂(μ‐oxamidate)}⁺ ( 1 ⁺) and {Mo₂(DAniF)₃]₂(μ‐dithiooxamidate)}⁺ ( 2 ⁺; DAniF=N,N′‐di(p‐anisyl)formamidinate)—are significantly differentiated in terms of electronic coupling between the two [Mo₂] units. For 1 ⁺ the intervalence (IV) charge‐transfer band in the near‐IR spectrum is truncated in half on the low‐energy side as predicted for MV compounds at the Class II–III limit (2H_ab/λ=1; for which H_ab=electronic coupling matrix element and λ=reorganization energy). In contrast, the very strongly coupled analogue 2 ⁺, as indicated by 2H_ab/λ=3.5 (> >1), exhibits a higher energy and more symmetrical IV band. As rare examples, this pair of MV species shows distinct optical behaviors for MV systems crossing the Class III region. Optical analysis and DFT calculations are carried out to elucidate the transformation from vibronic to electronic vertical transition.     

Theoretical study of direct dissociative charge exchange at low energy (1–100 eV)

A theoretical investigation of the direct dissociative charge exchange process in ion—molecule collisions at low energy (1–100 eV) is presented. The process is described within the semiclassical impact parameter framework in terms of transitions between vibronic states. The initial vibrational state ν of the molecule undergoing dissociation decays owing to interaction with the vibrational continuum ϵ in which it is embedded. In view of the nearly resonant characteristics of the process, the ν−ϵ interaction h_ν(ϵ) is assumed to behave like a function of the relative ion—molecule coordinates R and γ of the form A(ϵ)f(γ)R exp(− λR. Both isotropic (f(γ) = 1) and anisotropic (f(γ) = cos γ or sin γ) interactions are investigated. The problem is first solved in closed analytical form for model cases in the weak and strong coupling limits. Computer simulations are then performed on various prototype cases in order to provide examples illustrating the role of both the discrete—continuum energy differences Δ_ν(ϵ, R) and the coupling strength, as well as to illustrate typical dependences of the direct dissociative charge exchange spectra on collision energy, impact parameter and orientation of the molecular axis with respect to the incident beam direction.     

Nonadiabatic scattering of NO off Au3 clusters: A simple and robust diabatic state manifold generation method for multiconfigurational wavefunctions

The presence of nonadiabatic effects during the interaction of small molecules with metals has been observed experimentally for the last decades. Specially remarkable are the effects found for NO/Au, where experiments have suggested the presence of very strong vibronic coupling during the molecular scattering. However, the accurate inclusion of the nonadiabatic effects in periodic boundary conditions (PBC) theoretical methods remain an unapproachable challenge. Here, aiming to give some theoretical insight to the strong vibronic coupling, we have adopted a pragmatic point of view, taking use of an auxiliary simplified system, NO/Au₃. We show the importance of nonadiabatic coupling, during the scattering of NO from a Au₃ cluster, using a diabatic representation of 12 electronic states of the system, including a few charge-transfer states. Our diabatic representation is obtained by rotating the orbital and configuration interaction (CI) vectors of a restricted active space (RAS) wavefunction. We present a strategy for extracting the best effective manifold of states relevant to the system, below some prescribed energy, directly from the RAS CI vectors. This scheme is able to disentangle a large dense manifold of adiabatic states with strong coupling and crossings. This approach is also shown to work for multireference configuration interaction (MRCI). By performing quantum propagations, we observed an increase in vibrational redistribution with increasing initial vibrational or translational energies. We suggest that these nonadiabatic effects should also be present at smaller energies in larger clusters. © 2018 Wiley Periodicals, Inc.     

Effect of magnetic exchange,double exchange,vibronic coupling,and asymmetry on magnetic properties in d2–d3 mixed‐valence dimers

The effect of magnetic exchange, double exchange, vibronic coupling, and asymmetry on magnetic properties of d²–d³ systems is discussed. The temperature‐dependent magnetic moment was calculated with the semiclassical adiabatic approach. The results show that the vibronic coupling from the out‐of‐phase breathing vibration on the metal sites (Piepho, Krausz, and Schatz [PKS] model) and the vibronic coupling from the stretching vibration between the metal sites (P model) favor the localization and delocalization of the “extra” electron in mixed‐valence dimers, respectively. The magnetic properties are determined by the interplay among magnetic exchange, double exchange, and vibronic coupling. The results obtained by analyzing d²–d³ systems can be generalized to other full delocalized dinuclear mixed valence systems with a unique transferable electron. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Xanthone. II. Vibronic coupling analysis from high resolution phosphorescence spectra

High resolved phosphorescence spectra of xanthone have been recorded in four host matrices in order to study vibronic coupling between the lowest tripl origin in all hosts, and the energetically close-lying second triplet state T₂, which is of nπ* orbital origin. In three hosts, there is thermall to phosphorescence from T₁. Vibrational analyses of the two emissions are reported. The vibrational structure of both emissions depends little on t vibronic mixing between the lowest two triplet states is weak, in spite of the small energy separation in some hosts. The importance of the different i ₁ and its sublevels is discussed, and it is concluded that across energy separations smaller than about 200 cm^?1 spin—orbit mixing is more orbital mixing between the ³ππ* and ³nπ* configurations of xanthone.     

Vibronic coupling effects in trimeric mixed-valence clusters

The spectrum of a trimeric mired-valence cluster d₁–d₁–d₂ is calculated in the Piepha-Krausz-Schatz vibronic model. Based on the vibronic spectra obtained magnetic properties of the d₁–d₁–d₂ cluster are investigated It is shown that spin of the system's ground state may change not only as a result of double exchange reduction by vibronic coupling, but also due to a diflerence in the eneqy dependence of the lowest vibronic states on the vibronic coupling constant for diflerent total spin values. Unlike previous studies of vibronic interactions in the d₁–d₁–d₂ cluster, in this study the diagonalizations of the vibronic-coupling and double-exchange matrices are fuljilled simultaneously, using Lanczos' method. Due to this, all types 4 vibronic state mixing by double exchange could be taken into account properly.Moldova State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 5, pp. 20–32, September–October, 1993.Translated by L. Smolina     

Zwitterionic Mixed Valence: Internalizing Counteranions into a Biferrocenium Framework toward Molecular Expression of Half-Cells in Quantum Cellular Automata

Realization of molecular quantum cellular automata (QCA), a promising architecture for molecular computing through current-free processes, requires improved understanding and application of mixed-valence (MV) molecules. In this report, we present an electrostatic approach to creating MV subspecies through internalizing opposite charges in close proximity to MV ionic moieties. This approach is demonstrated by unsymmetrically attaching a charge-responsive boron substituent to a well-known organometallic MV complex, biferrocenium. Guest anions (CN⁻ and F⁻) bind to the Lewis acidic boron center, leading to unusual blue-shifts of the intervalence charge-transfer (IVCT) bands. To the best of our knowledge, this is the first reported example of a zwitterionic MV series in which the degree of positive charge delocalization can be varied by changing the bound anions, and serves to clarify the interplay between IVCT parameters. The key underlying factor is the variable zero-level energy difference in the MV states. This work provides new insight into imbuing MV molecules with external charge-responsiveness, a prerequisite of molecular QCA techniques.     

Acetylene-insertion reactions into Pt(II)–H and Pt(II)–SiH3 bonds. An ab initio MO study and analysis based on the vibronic coupling model

Acetylene insertion into Pt(II)–H and Pt(II)SiH₃ bonds of PtH(SiH₃)(PH₃) was investigated using ab initio molecular orbital and M?ller-Plesset perturbation theory methods. The insertion into PtH was predicted to proceed with a smaller activation energy (E _a =12.8 kcal/mol) than that into PtSiH₃ (E _a =20.9 kcal/mol). The reaction energy (ΔE) of the insertion into PtH is 10 kcal/mol smaller than that for the insertion into PtSiH₃, which reflects differences in bond energies between CH and CSi and between PtH and PtSiH₃. A comparison with ethylene insertion revealed that the acetylene insertion occurs more easily, and the latter reaction is more exothermic. A simple vibronic coupling model combined with Toyozawa's interaction mode analysis was used to examine interesting differences in E _a and ΔE between insertions into PtH and PtSiH₃, and between acetylene and ethylene insertions. This analysis suggests that the factors determining E _a are the stiffness of the PtH and PtSiH₃ bonds and the vibronic coupling strength of acetylene and ethylene. Received: 13 August 1998 / Accepted: 2 September 1998 / Published online: 15 February 1999     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

The matrix theory of electron spin multiplets for atoms and molecules

In this article a matrix method for the construction of spin multiplets (spinconfigurations) is suggested in order to solve the multielectron problem for atoms and mulecules by means of configuration interaction.A simple graphical way is given to enumerate configurations and to break their set into subsets of configurations related to the given projection of the total spin of a system S _z . It is found that all matrices in the theory of spin multiplets are convex and in cases of two, three, and four electrons are broken into blocks of an order no higher than 3.The model of the solution of the multielectron Schrödinger equation, in which the total spin of core electrons is zero, is considered. In this model the construction of linear combinations of configurations is reduced to the construction of those for but valence electrons.     

List of subjects

The quantum yields of fluorescence and intersystem crossing in pyrazine-h₄ and -d₄ and pyrimidine vapors have been studied at moderately high pressures (50–100 Torr) in the presence of a foreign gas as a function of excitation energy in the S₁ (n, π*) ← S_o absorption region. The fluorescence quantum yield of pyrazine fluctuates in the lower energy region, but on the average is constant over the range of the excess vibrational energy 0–4000 cm^?1, whereas the fluorescence yield of pyrimidine decreases smoothly with increasing excess energy. For each of the three molecules, the intersystem crossing yield is approximately constant with a value near unity in a wide range of the excess energy, indicating that the intramolecular nonradiative transition from S₁ is governed by the crossing to the triplet state. From a calculation based on the first-order vibronic coupling (Herzberg-Teller) theory the radiative rate constant of the pyrazine fluorescence is found to be relatively large for the vibronic levels involving a non-totally symmetric vibration, ν₁₀₂. This accounts for the fluctuation of the fluorescence yields of pyrazine-h₄ and -d₄.     

A new spin-specific mechanism of attractive vibronic interaction

An interesting new type of spin-specific vibronic coupling is found. The non-adiabatic coupling induces an effective attractive interaction which softens the orginal repulsive interaction between a pair of electrons. The relation with the Cooper pair of superconducting electrons is discussed.     

Exchange coupling in alkoxy-polyoxovanadates [VIVnVV6?nO7(OR)12]4?n (n = 4, 3, 2)

The molecular structure and magnetic properties of alkoxy-polyoxovanadates [V^IV _n V^V _6−n O₇(OR)₁₂]⁴⁻ⁿ (n = 4, 3, 2) were studied within the framework of the DFT approach. The equilibrium geometric configurations of all complexes studied in this work are characterized by a distorted octahedral hexavanadate core; the unpaired d-electrons are localized on the metal centers (V^IV). The localized spin density distribution is also retained in the low-temperature crystal structures of the compounds whose magnetic properties are described by the Heisenberg-Dirac-van Vleck exchange spin Hamiltonian. The exchange parameters calculated using the broken symmetry formalism suggest predominance of ferromagnetic coupling between vanadium(IV) ions in the μ-OR bridged dimeric units {V^IVO(OR)V^IV} and in the diagonal pairs {V^IVOV^IV} (n = 4). The results obtained indicate that the magnitude and sign of the exchange parameters in the isostructural dimeric units within the hexavanadate core depend on the total number of unpaired electrons in the system.     

The Importance of Vibronic Coupling for Efficient Reverse Intersystem Crossing in Thermally Activated Delayed Fluorescence Molecules

Factors influencing the rate of reverse intersystem crossing (k_rISC) in thermally activated delayed fluorescence (TADF) emitters are critical for improving the efficiency and performance of third‐generation heavy‐metal‐free organic light‐emitting diodes (OLEDs). However, present understanding of the TADF mechanism does not extend far beyond a thermal equilibrium between the lowest singlet and triplet states and consequently research has focused almost exclusively on the energy gap between these two states. Herein, we use a model spin‐vibronic Hamiltonian to reveal the crucial role of non‐Born‐Oppenheimer effects in determining k_rISC. We demonstrate that vibronic (nonadiabatic) coupling between the lowest local excitation triplet (³LE) and lowest charge transfer triplet (³CT) opens the possibility for significant second‐order coupling effects and increases k_rISC by about four orders of magnitude. Crucially, these simulations reveal the dynamical mechanism for highly efficient TADF and opens design routes that go beyond the Born‐Oppenheimer approximation for the future development of high‐performing systems.     

The origin of energy functional in Roothaan open shell SCF theory

Different methods of averaging of energy over the states of electronic configurations γ^N (n_γ = 1, 2, 3 and N = 1, 2, …, 2n_γ ? 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t^N (N = 2–4) and e² there exist states for which VCC are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such “non-Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.     

Excited state dynamics and spectroscopy of the 1A″ state of NSF vapor — comparisons with SO2

The fluorescence emission spectrum and analysis of NSF vapor is presented. Single vibronic level excitation near the S₁ origin gives rise to a 10 μs radiative decay. The fluorescence lifetime for excitation of levels with ? 4500 cm^?1 excess vibrational energy becomes controlled by a unimolecular radiationless process which is likely photodissociation; the dependence of this radiationless rate on energy and vibrational mode is investigated. The perturbations resulting from coupling of zero-order S₁ states with other vibronic levels which control the excited state dynamics of SO₂ are apparently not operative for NSF. Attempts are made to rationalize the grossly different dynamic behavior of the S₁ levels of these two otherwise very similar systems.     

Magnetic ordering and metal‐atom site preference in tetragonal CrMnAs: Electronic correlation effects

The electronic and magnetic structures of tetragonal, Cu₂Sb‐type CrMnAs were examined using density functional theory. To obtain reasonable agreement with reported atomic and low‐temperature magnetic ordering in this compound, the intra‐atomic electron–electron correlation in term of Hubbard U on Mn atoms are necessary. Using GGA + U, calculations identify four low‐energy antiferromagnetically ordered structures, all of which adopt a magnetic unit cell that contains the same direct Cr Cr and Cr Mn magnetic interaction, as well as the same indirect Mn⋅⋅⋅Mn magnetic interaction across the Cr planes. One of these low‐energy configurations corresponds to the reported case. Effective exchange parameters for metal–metal contacts obtained from SPRKKR calculations indicate both direct and indirect exchange couplings play important roles in tetragonal CrMnAs. © 2018 Wiley Periodicals, Inc.     

Ab initio Hartree–Fock and configuration-interaction treatment of the interaction between two nickel atoms

The interaction between two nickel atoms in the configurations (3d)⁸(4s)² and (3d)⁹ (4s)¹ has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσ_g molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.     

A Study of Intramolecular Energy Transfer in Conformationally Rigid molecules with stereoisomerically oriented donor and acceptor groups

The indanono naphthaleno compounds 1 , 3 , 5 and 7 exhibit, on both irradiation in the ¹L_b band (315 nm) and the n → π* transition (> 340 nm) in EPA at 77° K, neither fluorescence from naphthalene nor phosphorescence from indanone, but exclusively phosphorescence from naphthalene, and quenching in liquid solution with 1,3-pentadiene results in triplet energy transfer from the naphthaleno group only. The naphthalene phosphorescence exhibited by the ketones ( 1 , 3 , 5 , 7 ) has an enhanced quantum efficiency with respect to that on direct excitation of the corresponding hydrocarbons ( 2 , 4 , 6 , 8 ) and more strongly in the exo than in the endo orientation. In order to account for the energy wasting in the intramolecular triplet energy transfer in the endo compounds, a transfer route via a weak triplet donor-acceptor exciplex, specific to through-space interaction in the endo configuration (providing for additional radiationless T → S energy dissipation through vibrational coupling), competing with an efficient through-σ-bond exchange transfer mechanism operative in both configurations is proposed.     

Double exchange in polynuclear mixed-valence clusters. 1. General solution of the electronic problem

The problem of calculating the electronic energy spectra of mixed-valence clusters with one “extra” electron (dⁿ-dⁿ...dⁿ⁺¹) or hole (dⁿ⁺¹-dⁿ⁺¹...dⁿ) delocalized in the paramagnetic cores of transition metals is solved. Unlike the available particular solutions, which are restricted to small numbers of ions and electrons, the solution proposed in this work is general and is suitable for many-electron systems of arbitrary numbers of nuclei and arbitrary symmetries. The new microscopic approach to the double exchange problem is based on the combination of the sequential (“chain”) scheme of spin coupling and angular momentum method. In terms of this approach, an analytical dependence of the matrix elements of the double exchange, Heisenberg exchange, and vibronic interaction on all spin quantum numbers is obtained. The final equations contain only the 6j symbols and are free of the higher-order nj symbols, which obstructed the solution of the double exchange problem in previous works. Valencia University, Spain. Bordeaux University, France. Moldova State University. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 5, pp. 805–815, September–October, 1996. Translated by I. Izvekova