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     

Formation and infrared spectroscopic characterization of carbon suboxide complexes TM-η1-C3O2 and the inserted ketenylidene complexes OCTMCCO (TM=Cu,Ag, Au) in solid neon

The reactions of coinage metal atoms Cu, Ag and Au with carbon suboxide (C₃O₂) are studied by matrix isolation infrared spectroscopy. The weakly bound complexes TM-η¹-C₃O₂ (TM=Cu, Ag, Au), in which the carbon suboxide ligand binds to the metal center in the monohapto fashion are formed as initial reaction products. The complexes subsequently isomerize to the inserted products OCTMCCO upon visible light (λ = 400–500 nm) excitation. The analysis of the electronic structure using modern quantum chemistry methods suggests that the linear OCTMCCO complexes are best described by the bonding interactions between the TM⁺ cation in the electronic singlet ground state and the [OC…CCO]⁻ ligands in the doublet state forming two TM⁺ ← ligands σ donation and two TM⁺ → ligands π backdonation bonding components. In addition, the CuCCO, AgCCO and AuCCO complexes are also formed, which are predicted to be bent.     

The Oxygen‐Rich Beryllium Oxides BeO4 and BeO6

Two novel isomers of BeO₄ with the structures OBeOOO and OBe(O₃) in the electronic triplet state have been prepared as well as the known disuperoxide complex Be(O₂)₂ in solid noble‐gas matrices. We also report the synthesis of the oxygen‐rich bis(ozonide) complex Be(O₃)₂ in the triplet state which has a D_2d equilibrium geometry. The molecular structures were identified by infrared absorption spectroscopy with isotopic substitutions as well as quantum chemical calculations.     

Absolute quantum yield measurements for the formation of oxygen atoms after UV laser excitation of SO2 at 222-4 nm

The dynamics of formation of oxygen atoms after UV photoexcitation of SO₂ in the gas-phase was studied by pulsed laser photolysis-laser-inducedfluorescence ‘pump-and-probe’ technique in a flow reactor. SO₂ at room-temperature was excited at the KrCl excimer laser wavelength (222.4 nm) and O(³P_j) photofragments were detected under collision-free conditions by vacuum ultraviolet laser-induced fluorescence. The use of narrow-band probe laser radiation, generated viaresonant third-order sum-difference frequency conversion of dye laser radiation in Krypton, allowed the measurement of the nascent O(³P_j=2,1,0) fine-structure state distribution:n _j=2/n_j=1/n_j=0 = (0.88 ± 0.02)/(0.10 ± 0.01)/(0.02 ± 0.01). Employing NO₂photolysis as a reference, a value of Φ₀(³P) = 0.13 ± 0.05 for the absolute O(³P) atom quantum yield was determined. The measured O(³P) quantum yield is compared with the results of earlier fluorescence quantum yield measurements. A suitable mechanism is suggested in which the dissociation proceeds via internal conversion from high rotational states of the initially excited SO₂(~C¹B₂ (1, 2, 2) vibronic level to nearby continuum states of the electronic ground state.     

Multicomponent Molecular Orbital–Climbing Image–Nudged Elastic Band Method to Analyze Chemical Reactions Including Nuclear Quantum Effect

To analyze the H/D isotope effects on hydrogen transfer reactions in XHCHCHCHY?XCHCHCHYH (X, Y=O, NH, or CH₂) including the nuclear quantum effect of proton and deuteron, we propose a multicomponent molecular orbital‐climbing image‐nudged elastic band (MC_MO–CI–NEB) method. We obtain not only transition state structures but also minimum‐energy paths (MEPs) on the MC_MO effective potential energy surface by using MC_MO–CI–NEB method. We find that nuclear quantum effect affects not only stationary‐point geometries but also MEPs and electronic structures in the reactions. We clearly demonstrate the importance of including nuclear quantum effects for H/D isotope effect on rate constants (k_H/k_D).     

Quantum dynamics of dissociative adsorption of H2 and D2: The time-dependent wave packet method

A time-dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H₂ and D₂ on a flat and static surface. The molecule-surface interaction is described using a modified London-Eyring-Polanyi-Sato (LEPS) type potential for the H₂/Ni(100) system. The three-dimensional (3-D) dissociation probabilities were calculated for different initial rovibrational states as a function of initial incident energies. Our results show that the dissociation of the diatomic rotational states whose quantum numbers satisfyj+m = odd is forbidden at low energies for the homonuclear H_z and D₂ due to the selection rule. The effect of the rotational orientation of diatoms on adsorption predicts that the in-plane rotation (m = j) is more favorable for dissociation than the out-of-plane rotation (m = 0). Enhanced dissociation for vibrationally excited molecules and the significant enhancement of the dissociation probability of H2 when compared to D₂ were explained reasonably in terms of quantum mechanical zero-point energies, the tunneling effect and the reflection from an activation barrier. Project supported by the National Natural Science Foundation of China (Grant No. 19694033) and partially by the Science Foundation for Overseas Chinese Scholars and Students, administered by the State Education Commission of China (Grant No. 1992), by the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University at Changchun (Grant No. 98011, and by the Natural Science Foundation of Shandong Province (Grant No. Y96B03022)     

Are Triphenylamine‐Functionalized or Carbazole‐Functionalized Iridium Complexes the More Effective Phosphorescent Materials? A Theoretical Perspective

The ground and excited states, charge injection/transport, and phosphorescence properties of eleven carbazole‐ and triphenylamine‐functionalized Ir^III complexes were investigated by using the DFT method. By analyzing the spin–orbit coupling (SOC) matrix elements, radiative decay rate constants k_r, and the electronic structures and energies at the ${{\rm{S}}_{\rm{0}}^{{\rm{opt}}} }$ and ${{\rm{T}}_{\rm{1}}^{{\rm{opt}}} }$ states, it was possible to rationalize the order of the experimental phosphorescence quantum yields of a series of Ir^III complexes and to predict that [Ir(Nph‐2‐Cz‐tz)₃] has a higher phosphorescence quantum yield than [Ir(TPA‐tz)₃] (TPA=triphenylamine, tz=thiazolyl, Cz=carbazole, Nph=N‐phenyl). Carbazole‐functionalized Ir^III complexes were shown to be efficient phosphorescent materials that have not only fast but also balanced electron/hole‐transport performance as well as high phosphorescence quantum yields. The phosphorescence emission spectra can be modulated by modifying or replacing a pyridyl substituent.     

Theoretical study on S<Subscript>1</Subscript>(<Superscript>1</Superscript>B<Subscript>3u</Subscript>) state electronic structure and absorption spectrum of pyrazine

Making use of a set of quantum chemistry methods, the harmonic potential surfaces of the ground state (S₀(¹ A _g)) and the first (S₁(¹ B _3u)) excited state of pyrazine are investigated, and the electronic structures of the two states are characterized. In the present study, the conventional quantum mechanical method, taking account of the Born-Oppenheimer adiabatic approximation, is adopted to simulate the absorption spectrum of S₁(¹ B _3u) state of pyrazine. The assignment of main vibronic transitions is made for S₁(¹ B _3u) state. It is found that the spectral profile is mainly described by the Franck-Condon progression of totally symmetric mode ν_6a. For the five totally symmetric modes, the present calculations show that the frequency differences between the ground and the S₁(¹ B _3u) state are small. Therefore the displaced harmonic oscillator approximation along with Franck-Condon transition is used to simulate S₁(¹ B _3u) absorption spectra. The distortion effect due to the so-called quadratic coupling is demonstrated to be unimportant for the absorption spectrum, except the coupling mode ν_10a. The calculated S₁(¹ B _3u) absorption spectrum is in reasonable agreement with the experimental spectra. Supported by Taiwan National Science Council (Grant Nos. NSC 96-2113-M-009-021 and NSC 96-2811-M-009-023)     

Quantum dynamics calculation of reaction probability for H + Cl2 → HCl + Cl

We present in this paper a time-dependent quantum wave packet calculation of the initial state selected reaction probability for H + Cl₂ based on the GHNS potential energy surface with total angular momentumJ = 0. The effects of the translational, vibrational and rotational excitation of Cl₂ on the reaction probability have been investigated. In a broad region of the translational energy, the rotational excitation enhances the reaction probability while the vibrational excitation depresses the reaction probability. The theoretical results agree well with the fact that it is an early down-hill reaction.     

Best molecular multiple quantum bit for the diatomic molecular quantum computer using potassium nitride and calcium nitride through vibrational progression

In this article, based on the former accurate and precise ab initio calculation results for potassium nitride (KN) and calcium nitride (CaN), I revisit the possibilities and potentials of KN and CaN as the best candidate for molecular multiple quantum bit (MMQB) for the diatomic molecular quantum computer (DMQC), and would like to propose the two molecules as CPUs of the DMQC. Lowest lying four electronic states of CaN are energetically located within 1800 cm^?1. These four states form the good molecular electronic two quantum bits through the dipole and weak spin–orbit interactions. ³Π state of KN is calculated to lie above ground ³Σ^? state by 177 cm^?1. KN is a promising candidate for an electronic one quantum bit. When vibrational progression is considered to be accompanied by the electronic transition, CaN and KN are good candidates for larger MMQBs up to a thousand even in the single molecule because the concrete quantum state bearing the quantum bit is each molecular ro‐vibronic state, that is, the specific rotational state on each vibronic level. When CaN and KN work in assemblies as quantum bit, those assemblies become larger MMQBs, the number of which might reach the Avogadro number because the molecular spectra appearing in the molecular spectroscopy are the results from the observation by the photon‐exchange among intramolecular quantum states made up of 10¹⁵ to the Avogadro (6.02 × 10²³ mol^?1) number of molecules interacting with radiation. Even without the vibrational progression, in the case of the lowest two quantum bit of KN, which is a stable vibronic two quantum bit, a thousand of KN molecules provide a thousand of MMQBs. That is the same situation as that for CaN. Using KN and CaN as MMQBs (playing the triple roles of CPU, RAMs (memory), and storages) ultra‐fast “in core” quantum computation can be done. An application of the full‐CI quantum chemistry calculation results for the demonstration of the DMQC is discussed. I strongly hope that the MMQB will “oscillate” and that the DMQC will be realized in the near future for the welfare of human being and the further development of modern material civilization. © 2014 Wiley Periodicals, Inc.     

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

In this work, we study the position and momentum information entropies of multiple quantum well systems in fractional Schrödinger equations, which, to the best of our knowledge, have not so far been studied. Through a confining potential, their shape and number of wells (NOW) can be controlled by using a few tuning parameters; we present some interesting quantum effects that only appear in the fractional Schrödinger equation systems. One of the parameters denoted by the L_d can affect the position and momentum probability densities if the system is fractional (1 < α < 2). We find that the position (momentum) probability density tends to be more severely localized (delocalized) in more fractional systems (ie, in smaller values of α). Affecting the L_d on the position and momentum probability densities is a quantum effect that only appears in the fractional Schrödinger equations. Finally, we show that the Beckner Bialynicki-Birula-Mycieslki (BBM) inequality in the fractional Schrödinger equation is still satisfied by changing the confining potential amplitude V_conf, the NOW, the fractional parameter α, and the confining potential parameter L_d .     

Femtosecond Dynamics in the Lactim Tautomer of Phycocyanobilin: A Long‐Wavelength Absorbing Model Compound for the Phytochrome Chromophore

Transient UV/Vis absorption spectroscopy is used to study the primary dynamics of the ring‐A methyl imino ether of phycocyanobilin (PCB‐AIE), which was shown to mimic the far‐red absorbance of the Pfr chromophore in phytochromes (R. Micura, K. Grubmayr, Bioorg. Med. Chem. Lett.­ 1994, 4, 2517–2522 ). After excitation at 615 nm, the excited electronic state is found to decay with τ₁=0.4 ps followed by electronic ground‐state relaxation with τ₂=1.2 and τ₃=6.7 ps. Compared with phycocyanobilin (PCB), the initial kinetics of PCB‐AIE is much faster. Thus, the lactim structure of PCB‐AIE seems to be a suitable model that could not only explain the bathochromic shift in the ground‐state absorption but also the short reaction of the Pfr as compared to the Pr chromophore in phytochrome. In addition, the equivalence of ring‐A and ring‐D lactim tautomers with respect to a red‐shifted absorbance relative to the lactam tautomers is demonstrated by semiempirical calculations.     

Comparative study of the photoassociation reaction of He + X+→ HeX+ (X = H,D): Including multiphoton transitions and dissociations

Using the time-dependent quantum wave packet method, the photoassociation (PA) processes of He + H ⁺→ HeH⁺ and He + D ⁺→ HeD⁺, driven by the sin²-shaped femtosecond laser pulse in the electronic ground state, including multiphoton transitions and dissociations, are investigated for a wide range of initial collision momenta spanning from 1 to 4 a.u. (or for the collision energy roughly in the ranges of 0.009∼0.148 eV and 0.006∼0.089 eV for HeH⁺ and HeD⁺ systems, respectively). It is found that, at some collision momenta, multiphoton transitions to deeply bound states are inevitable to occur and can greatly decrease the PA probability of the target state that selected is the vibrational state v = 6. For the dissociation process, the higher-order (two- and three-photon) dissociations, measured from the target state, tend to be significant at relative high collision energies, which implies that above-threshold dissociations may also be an important loss mechanism in the PA process. In addition, it is also shown that the higher-order dissociation is much stronger for HeH⁺ systems than that for HeD⁺ systems at a given collision momentum, and could be enhanced by the strong transitions among deeply bound states.     

Real wave packet and flux analysis studies of the H + F2 → HF + F reaction

The H + F₂ → HF + F reaction on ground state potential energy surface is investigated using the quantum mechanical real wave packet and Flux analysis method based on centrifugal sudden approximation. The initial state selected reaction probabilities for total angular momentum J = 0 have been calculated by both methods while the probabilities for J > 0 have been calculated by Flux analysis method. The initial state selected reaction probabilities, integral cross sections and rate coefficients have been calculated for a broad range of collision energy. The results show a large rotational enhancement of the reaction probability. Some resonances were seen in the state‐to‐state reaction probabilities while state‐to‐all reaction probabilities and the reaction cross section do not manifest any oscillations and the initial state selected reaction rate constants are sensitive to the temperature. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Critical stability and quantum phase transition of screened two-electron system

The ground state energy and structural properties of a model two-electron system (Zee), bound via screened Coulomb interaction with nuclear charge Z, have been studied under the variational framework. Hylleraas type basis has been adopted for explicit incorporation of the electron–electron correlation. Critical nuclear charges (Z_c) of Zee system have been reported for different screening parameters (μ). Expectation values of different structural properties have been estimated to predict the internal structure of the Zee system. The variation of the structural properties with respect to Z for different μ reveals the signature of quantum phase transition (QPT) in the vicinity of Z_c. Moreover, the nature of variation of these properties with respect to Z in case of bare Coulomb or free system (μ = 0) is completely opposite to those of screened system (μ ≠ 0). Radial two-particle density (TPD) confirms the symmetry breaking of the electronic structure and therefore QPT in the vicinity of Z_c.     

1H-Phenalen-1-one: Photophysical Properties and Singlet-Oxygen Production

The efficiency of aromatic ketones as singlet-oxygen (¹O₂(¹Δ_g)) sensitizers can vary considerably with the electronic configuration of their lowest triplet state and the solvent used. Near-infrared measurements of tie luminescence of singlet oxygen have shown that the quantum yield of singlet-oxygen production (Φ_Δ) by 1H-phenalen-1-one ( 1 ) is close to unity in both polar (Φ_Δ = 0.97±0.03 in methanol) and non-polar solvents (Φ_Δ = 0.93±0.04 in benzene). Analysis of the absorption spectra of the ground state and phosphorescence measurements show that the lowest singlet and triplet states have dominant π, π* electronic configurations. The quantum yield of intersystem crossing (Φ_ISC) of 1 , determined by laser flash photolysis (partial-saturation method), is equal to unity. In comparison with other aromatic ketones, these parameters are important for the discussion of the surprisingly high Φ_ISC of 1 and the efficient energy transfer from its triplet state to molecular oxygen. The 1H-phenalen-1-one ( 1 ), being one of the most efficient singlet-oxygen sensitizers in both polar and non-polar media, could be used as a reference sensitizer, in particular in the area of relatively high energies of excitation.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.