Average inner and outer radii in singly-excited 1<Emphasis Type="Italic">snl</Emphasis> states of the He atom

Average inner < r _< > and outer < r _> > radii are studied for 28 singly-excited 1 snl singlet and triplet states (0 ≤ l ≤ n ≤ 5) of the He atom. In all the cases, the average inner radius < r _< > is close to 0.75 bohr, which indicates that one of the two electrons behaves like the 1s electron in He⁺. On the other hand, an analysis of the average outer radius < r _> > shows that the other electron of the 1snl states behaves approximately like an snl electron in the hydrogen atom. The average outer radius < r _> > reflects more diffuse character of the singlet electron distribution. This paper is dedicated to the late Professor Serafin Fraga for his great contribution to quantum sciences. Contribution to the Serafin Fraga Memorial Issue.     

Quantum crystallography: A perspective

Extraction of the complete quantum mechanics from X‐ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X‐ray diffraction data into an electron density that reflects the antisymmetry of an N‐electron wave function. A formalism for this was developed early on for the determination of a constrained idempotent one‐body density matrix. The formalism ensures pure‐state N‐representability in the single determinant sense. Applications to crystals show that quantum mechanical density matrices of large molecules can be extracted from X‐ray scattering data by implementing a fragmentation method termed the kernel energy method (KEM). It is shown how KEM can be used within the context of quantum crystallography to derive quantum mechanical properties of biological molecules (with low data‐to‐parameters ratio). © 2017 Wiley Periodicals, Inc.     

The Photokinetics of Electron Transfer Reaction of Methylene Blue with Titanium Trichloride in Aqueous–Alcoholic Solvents

The kinetics of photoinduced electron transfer reaction of methylene blue (MB) and titanium trichloride was investigated in water and different aqueous–alcoholic solvents. The reaction is pseudo‐first order, dependent only on the concentration of titanium trichloride at a fixed concentration of MB. The effect of water and aqueous–alcoholic solvents was studied in the acidic pH range (4–7). It was observed that the quantum yield (ϕ ) of the reaction increased with increase in polarity of the reaction medium. The quantum yield was high under acidic conditions and decreased with further increase in acidity. The addition of ions and increase in temperature increased the rate and quantum yield of the reaction. The absence of any reaction intermediate was confirmed by spectroscopic investigations. A mechanism for the reaction has been proposed in accordance with the kinetics of the reaction. The activation energy (E _a) was calculated by the Arrhenius relation. Thermodynamic parameters such as E _a, enthalpy change (ΔH ), free energy change (ΔG ), and entropy change (ΔS ) were also evaluated.     

Bright,Fluorescent Dyes Based on Imidazo[1,2‐a]pyridines that are Capable of Two‐Photon Absorption

A library of imidazo[1,2‐a]pyridines was synthesized by using the Gevorgyan method and their linear and non‐linear optical properties were studied. Derivatives that contained both electron‐donating and electron‐withdrawing groups at the 2 position were comprehensively investigated. Their emission quantum yield ranged between 0.2–0.7 and it was shown to depend on the substitution pattern, most notably that on the phenyl ring. Electron‐donating substituents improved the luminescence performance of these compounds, whereas electron‐withdrawing substituents led to a more erratic behavior. Substitution on the six‐membered ring had less effect on the fluorescence properties. Extension of the delocalization increased the luminescence quantum yield. A new quadrupolar system was designed that contained two imidazo[1,2‐a]pyridine units on its periphery and a 1,4‐dicyanobenzene unit at its center. This system exhibited a large Stokes‐shifted luminescence that was affected by the polarity and rigidity of the solvent, which was ascribed to emission from an excited state with strong charge‐transfer character. This quadrupolar feature also led to an acceptable two‐photon absorption response in the NIR region.     

Theoretical study on regularity of changes in quantum defects in Rydberg state series of many‐valence electron atoms within WBEPM theory

Within the scheme of the weakest bound electron potential model theory, the regularity of changes in quantum defects in 40 “spectrum‐level‐like series” of several many‐valence electron atoms of the third period was studied. The n–δ curves of the 40 spectrum‐level‐like series could be classified into three types; for all such series the quantum defects δ could be expanded as a polynomial of the principal quantum number n in a spectrum‐level‐like series. With regularity, the level energies of high Rydberg states in a series can be predicted accurately. By carefully studying and explaining the three types of 40 n–δ curves, the conclusion was reached: the type of the n–δ curve, i.e., the regularity of changes in quantum defects in a spectrum‐level‐like series, was determined by both the energy level and the azimuthal quantum number l of the weakest bound electron. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 232–237, 2001     

Photopolymerization of cyclohexene oxide by use of o-nitrobenzyl triphenylsilyl ether/aluminum compound catalyst. Dependence of catalyst activity on the structure of the silyl ether

o-Nitrobenzyl triphenylsilyl ehther/aluminum compound has been previously shown by the authors to act as catalyst in the photopolymerization of epoxides. The dependence of the structure of the silyl ether on the catalyst activity was examined. There were two steps in the photopolymerization. The first step (“Step 1”) is photodecomposition of the silyl ether to silanol. The second step (“Step 2”) is the initiation of polymerization by silanol and the aluminum compound. The introduction of an electron withdrawing group, Cl, CF₃, on the benzene ring bonded to Si made the quantum yield of Step 1 low, however, the rate of Step 2 was increased. The low quantum yield of Step 1 was explained in terms of the rate of electron transfer that is controlled by the relative electron density between the CH₂ and NO₂ in the o-nitrobenzyl group. The acceleration of Step 2 was explained in terms of an increase in silanol acidity that was promoted by the introduction of an electron withdrawing group. The overall rate of the photopolymerizatiol depends to a greater degree on the rate of Step 2 than on that of Step 1.     

A relation between energies of the short-lived negative ion states and energies of unfilled molecular orbitals for a series of bromoalkanes

A series of bromoalkanes was investigated by means of electron transmission spectroscopy in the gas phase. Experimental values of vertical electron affinities associated with occupation of the LUMO by an incoming electron were assigned using ab initio quantum chemical calculations. The predicted vertical electron affinity values differ from measured ones by at most ±0.2 eV. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1222–1224, June, 2007.     

MODELS FOR BACTERIAL PHOTOSYNTHESIS: ELECTRON TRANSFER FROM PHOTOEXCITED SINGLET BACTERIOPHEOPHYTIN TO METHYL VIOLOGEN AND m-DINITROBENZENE

Abstract. As a model for the primary reactions of photosynthesis, we studied photochemical electron transfer from bacteriopheophytin (BPh) to methyl viologen (MVC1₂) and to m-dinitrobenzene (m-DNB) in solution. Both MVC1₂ and m-DNB cause reductions in the lifetime of the first excited singlet state of BPh (BPh*), in the fluorescence quantum yield, and in the quantum yield of the triplet state, BPh ⁺. The quenching of BPh* probably results from electron transfer, which generates short-lived radical pairs involving the BPh radical cation (BPh⁺) and the reduced form of the quencher. Electron transfer from BPh* is thermodynamically favorable, but that from BPh^T is not. From the magnitude of the quenching, we calculate rate constants for electron transfer in collision complexes formed between BPh* and MVC1₂ or m-DNB. Measurements of the quantum yield of the free BPh⁺ radical indicate that about 3/4 of the [BPh⁺ MV⁺] radical pairs decay by reverse electron transfer, rather than dissociating to give the free radicals. Essentially all of the [BPh⁺m-DNB ⁺] radical pairs must decay by reverse electron transfer, because free BPh⁺ cannot be detected in this case. From these data, we estimate the rate constants for the reverse electron transfer reactions. The higher probability of dissociation in the [BPh⁺ MV⁺] radical pair can be explained by coulombic repulsion. The rate of the primary electron transfer reaction in photosynthetic bacteria is comparable to that of forward electron transfer in the BPh* collision complexes. Reverse electron transfer, however, is at least 10³-times slower in the radical pair formed in the bacterial reaction center than it is in [BPh⁺m-DNB^?], and more than 10⁴-times slower than in [BPh⁺ MV⁺]. The explanation for this dramatic and crucially important difference remains unclear, but several possibilities are discussed.     

EPR and Spectrophotometric Studies of Free Radicals (O2°−, °OH, BPD-MA°−) and Singlet Oxygen (1O2) Generated by Irradiation of Benzoporphyrin Derivative Monoacid Ring A

Abstract— Benzoporphyrin derivative monoacid ring A (BPD-MA), a chlorin-type molecule, is a new photosensitizer currently in phase II clinical trials for the treatment by pho-todynamic therapy of cancerous lesions, psoriasis and pathologic neovascularization. The photochemistry (type I and/or II) of BPD-MA has been studied in homogeneous solution and in aqueous dispersions of unilamellar liposomes of dipalmitoylphosphatidylcholine (DPPC) using electron paramagnetic resonance and spectrophotometric methods. When oxygen-saturated solutions of BPD-MA were illuminated with 690 nm light, singlet oxygen (¹O₂), superoxide anion radical (O₂^?), hydroxyl radical (OH) and hydrogen peroxide (H₂O₂) were formed. The BPD-MA generates ¹O₂ with a quantum yield of ca 0.81 in ethanolic solution. The quantum yield does not change upon incorporation of BPD-MA into liposomes of DPPC. The superoxide anion radical was generated by the BPD-MA anion radical (BPD-MA^?) via electron transfer to oxygen, and this process was significantly enhanced by the presence of electron donors. The rate of production of 0₂ was also dependent on the concentration of BPD-MA used (3-100 μM). The quantum yield of O₂^?was found to be 0.011 and 0.025 in aqueous solution and DPPC liposomes, respectively. Moreover, O₂^_upon dis-proportionation can generate H₂O₂ and ultimately the highly reactive OH via the Fenton reaction. In anaerobic homogeneous solution, BPD-MA^?was predominantly photoproduced via the self-electron transfer between the excited- and ground-state species. The presence of an electron donor significantly promotes the reduced form of BPD-MA. These findings suggest that the photodynamic action of BPD-MA may proceed via both type I and type II mechanisms.     

Fast quantum crystallography

Typical contemporary X-ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R-factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.     

Photo-induced interfacial electron transfer from CdSe quantum dots to surface-bound <Emphasis Type="Italic">p</Emphasis>-benzoquinone and anthraquinone

Here we report transient spectral red-shift and transient absorption enhancement of p-benzoquinone radical in the presence of CdSe quantum dots after 355 nm pulse laser excitation. The spectral shift was caused by surface-bound p-benzoquinone molecules while the transient absorption increase was due to interfacial electron transfer from CdSe quantum dots to p-benzoquinone molecules. In contrast, spectral shift and absorption increase were much less significant for anthraquinone in the presence of CdSe quantum dots due to their weak adsorption abilities.     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

原子价壳层电子量子拓扑指数与元素电负性的关系

在基态原子价壳层电子隐核图的基础上, 基于拓扑化学原理以及原子价壳层电子结构特征, 构建了原子价壳层电子量子拓扑指数(AEI), 它对基态原子实现唯一性表征, 结合原子价壳层电子平均化能(∑n_iE_i/∑n_i)等参数, 建立了一套新的元素电负性标度: X_N＝－0.588710AEI₁＋0.761214AEI₂＋0.154982(∑n_iE_i/∑n_i)－0.080929. 该式给出了周期表中氢至镅共95种元素的电负性, 结果表明新电负性标度X_N与Pauling电负性标度颇为一致. 进一步从原子价轨道量子拓扑指数确定了sp, sp², sp³杂化轨道的电负性. 新标度在元素和物质的结构-性质研究中具有一定的适用性.     

Colorless to Purple–Red Switching Electrochromic Anthraquinone Imides with Broad Visible/Near‐IR Absorptions in the Radical Anion State: Simulation‐Aided Molecular Design

The large redshift of near‐infrared (NIR) absorptions of nitro‐substituted anthraquinone imide (Nitro‐AQI) radical anions, relative to other AQI derivatives, is rationalized based on quantum chemical calculations. Calculations reveal that the delocalization effects of electronegative substitution in the radical anion states is dramatically enhanced, thus leading to a significant decrease in the HOMO–LUMO band gap in the radical anion states. Based on this understanding, an AQI derivative with an even stronger electron‐withdrawing dicyanovinyl (di‐CN) substituent was designed and prepared. The resulting molecule, di‐CN‐AQI, displays no absorption in the Vis/NIR region in the neutral state, but absorbs intensively in the range of λ=700–1000 (λ_max≈860 nm) and λ=1100–1800 nm (λ_max≈1400 nm) upon one‐electron reduction; this is accompanied by a transition from a highly transmissive colorless solution to one that is purple–red. The relationship between calculated radical anionic HOMO–LUMO gaps and the electron‐withdrawing capacity of the substituents is also determined by employing Hammett parameter, which could serve as a theoretical tool for further molecular design.     

Synthesis and Photophysical Properties of 3,6-Diphenyl-9-hexyl-9<Emphasis Type="Italic">H</Emphasis>-carbazole Derivatives Bearing Electron Withdrawing Groups

Summary. 3,6-Diphenyl-9-hexyl-9H-carbazole derivatives bearing electron withdrawing groups, such as the formyl or the nitro-group in 4-positions of the phenyl substituents, were prepared and characterized. Their photophysical properties were evaluated and compared with those of the unsubstituted counterpart 3,6-diphenyl-9-hexyl-9H-carbazole. The electron withdrawing groups bearing compounds exhibited considerable red shifts of the absorption and the emission maxima. While 3,6-di(4-nitrophenyl)-9-hexyl-9H-carbazole emitted in the orange region of the visible spectrum with its emission maximum peaking at 585 nm, 3,6-di(4-formylphenyl)-9-hexyl-9H-carbazole gave a pure blue emission with a luminescence quantum yield of 95% peaking at 450 nm. Observed features were explained using quantum mechanical calculations and organic light emitting diodes using the formylphenyl substituted compound as emissive layer were built demonstrating the practical applicability of this class of compounds.     

Atomic Partitioning of the MPn (n = 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach

Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA-MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

花状硫化铜的合成及其光电催化性能

通过硫化介孔Cu_2O微球得到花状Cu_xS纳米催化材料,并采用丝网印刷法制备出Cu_xS/FTO对电极。通过X射线衍射(XRD)、扫描电子显微镜(SEM)、透射电子显微镜(TEM)等表征手段对所得材料的结构和形貌进行了探究,同时系统考察了溶液浓度、硫化时间、催化剂印刷层数对Cu_xS/FTO电极的催化性能影响和所组装量子点敏化太阳电池的光电转换效率,其中基于Zn-Cu-In-Se量子点敏化的电池转换效率达8.80%,表现出花状Cu_xS优异的光电催化性能。     

Synthesis and Photophysical Properties of 3,6-Diphenyl-9-hexyl-9H-carbazole Derivatives Bearing Electron Withdrawing Groups

3,6-Diphenyl-9-hexyl-9H-carbazole derivatives bearing electron withdrawing groups, such as the formyl or the nitro-group in 4-positions of the phenyl substituents, were prepared and characterized. Their photophysical properties were evaluated and compared with those of the unsubstituted counterpart 3,6-diphenyl-9-hexyl-9H-carbazole. The electron withdrawing groups bearing compounds exhibited considerable red shifts of the absorption and the emission maxima. While 3,6-di(4-nitrophenyl)-9-hexyl-9H-carbazole emitted in the orange region of the visible spectrum with its emission maximum peaking at 585 nm, 3,6-di(4-formylphenyl)-9-hexyl-9H-carbazole gave a pure blue emission with a luminescence quantum yield of 95% peaking at 450 nm. Observed features were explained using quantum mechanical calculations and organic light emitting diodes using the formylphenyl substituted compound as emissive layer were built demonstrating the practical applicability of this class of compounds.     

Radical-Enhanced Intersystem Crossing in a Bay-Substituted Perylene Bisimide−TEMPO Dyad and the Electron Spin Polarization Dynamics upon Photoexcitation**

A 4-amino-2,2,6,6-tetramethyl-1-piperidinyloxyl (TEMPO) radical was attached to the bay position of perylene-3,4 : 9,10-bis(dicarboximide) (perylenebisimide, PBI) to study the radical-enhanced intersystem crossing (REISC) and electron spin dynamics of the photo-induced high-spin states. The dyads give strong visible light absorption (ϵ=27000 M⁻¹ cm⁻¹at 607 nm). Attaching a TEMPO radical to the PBI unit transforms the otherwise non-radiative decay of S₁ state (fluorescence quantum yield: Φ_F=2.9 %) of PBI unit to ISC (singlet oxygen quantum yield: Φ_Δ=31.8 %, Φ_F=1.6 %). Moreover, the REISC is more efficient as compared to the heavy atom effect-induced ISC (Φ_Δ=17.8 % for 1,8-dibromoPBI). For the dyad, ISC takes 245 ps and triplet state lifetime is 1.5 μs, much shorter than the native PBI (τ_T=126.6 μs). X- and Q-band time-resolved electron paramagnetic resonance spectroscopy shows that the exchange interaction in the photoexcited radical-chromophore dyad is larger than the triplet zero-field splitting (ZFS) and the difference of Zeeman energies of the radical and chromophore. The inversion of electron spin polarization from emissive to absorptive was observed and attributed to the initial completion of the quartet state population and the subsequent depopulation processes induced by the zero-field splitting.