H2 System

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Michael Baer - One of the best experts on this subject based on the ideXlab platform.

  • beyond born oppenheimer conical intersections and electronic nonadiabatic coupling terms
    2006
    Co-Authors: Michael Baer
    Abstract:

    Preface. Abbreviations. 1. Mathematical Introduction. I.A. The Hilbert Space. I.A.1. The Eigenfunction and the Electronic non-Adiabatic Coupling Term. I.A.2. The Abelian and the non-Abelian Curl Equation. I.A.3. The Abelian and the non-Abelian Div-Equation. I.B. The Hilbert Subspace. I.C. The Vectorial First Order Differential Equation and the Line Integral. I.C.1. The Vectorial First Order Differential Equation. I.C.1.1. The Study of the Abelian Case. I.C.1.2. The Study of the non-Abelian Case. I.C.1.3. The Orthogonality. I.C.2. The Integral Equation. I.C.2.1. The Integral Equation along an Open Contour. I.C.2.2. The Integral Equation along an Closed Contour. I.C.3. Solution of the Differential Vector Equation. I.D. Summary and Conclusions. I.E. Exercises. I.F. References. 2. Born-Oppenheimer Approach: Diabatization and Topological Matrix. II.A. The Time Independent Treatment for Real Eigenfunctions. II.A.1. The Adiabatic Representation. II.A.2. The Diabatic Representation. II.A.3. The Adiabatic-to-Diabatic Transformation. II.A.3.1. The Transformation for the Electronic Basis Set. II.A.3.2. The Transformation for the Nuclear Wave-Functions. II.A.3.3. Implications due to the Adiabatic-to-Diabatic Transformation. II.A.3.4. Final Comments. II.B. Application of Complex Eigenfunctions. II.B.1. Introducing Time-Independent Phase Factors. II.B.1.1. The Adiabatic Schrodinger Equation. II.B.1.2. The Adiabatic-to-Diabatic Transformation. II.B.2. Introducing Time-Dependent Phase Factors. II.C. The Time Dependent Treatment. II.C.1. The Time-Dependent Perturbative Approach. II.C.2. The Time-Dependent non-Perturbative Approach. II.C.2.1. The Adiabatic Time Dependent Electronic Basis set. II.C.2.2. The Adiabatic Time-Dependent Nuclear Schrodinger Equation. II.C.2.3. The Time Dependent Adiabatic-to-Diabatic Transformation. II.C.3. Summary. II.D. Appendices. II.D.1. The Dressed Non-Adiabatic Coupling Matrix. II.D.2. Analyticity of the Adiabatic-to-Diabatic Transformation matrix, A, in Space-Time Configuration. II.E. References. 3. Model Studies. III.A. Treatment of Analytical Models. III.A.1 Two-State Systems. III.A.1.1. The Adiabatic-to-Diabatic Transformation Matrix. III.A.1.2. The Topological Matrix. III.A.1.3. The Diabatic Potential Matrix. III. A.2. Three-State Systems. III.A.2.1. The Adiabatic-to-Diabatic Transformation Matrix. III.A.2 2. The Topological Matrix. III. A.3. Four-State Systems. III.A.3.1. The Adiabatic-to-Diabatic Transformation Matrix. III.A.3 2. The Topological Matrix. III.A.4 Comments Related to the General Case. III.B. The Study of the 2x2 Diabatic Potential Matrix and Related Topics. III.B.1. Treatment of the General Case. III.B.2. The Jahn-Teller Model. III.B.3. The Elliptic Jahn-Teller Model. III.B.4. On the Distribution of Conical Intersections and the Diabatic Potential Matrix. III.C. The Adiabatic-to-Diabatic Transformation Matrix and the Wigner Rotation Matrix. III.C.1. The Wigner Rotation Matrices. III.C.2. The Adiabatic-to-Diabatic Transformation Matrix and the Wigner dj-Matrix. III. D. Exercise. 4. Studies of Molecular Systems. IV.A. Introductory Comments. IV.B. Theoretical Background. IV. C. Quantization of the Non-adiabatic Coupling Matrix: Studies of ab-initio Molecular Systems. IV.C.1. Two-State Quasi-Quantization. IV.C.1.1. The {H2,H} System. IV.C.1.2. The {H2,O} System. IV.C.1.3. The {C2H2) Molecule. IV.C.2. Multi-State Quasi-Quantization. IV.C.2.1. The {H2,H} System. IV.C.2.2. The {C2,H} System. IV.D. References. 5. Degeneracy Points and Born-Oppenheimer Coupling Terms as Poles. V.A. On the Relation between the Electronic Non-Adiabatic Coupling Terms and the Degeneracy Points. V.B. The Construction of Hilbert Subspaces. V.C. The Sign Flips of the Electronic Eigenfunctions. V.C.1. Sign-Flips in Case of a Two-State Hilbert Subspace. V.C.2. Sign-Flips in Case of a Three-State Hilbert Subspace. V.C.3. Sign-Flips in Case of a General Hilbert Subspace. V.C.4 Sign-Flips for a case of a Multi-Degeneracy Point. V.C.4.1 The General Approach. V.C.4.2 Model Studies. V.D. The Topological Spin. V.E. The Extended Euler Matrix as a Model for the Adiabatic-to-Diabatic Transformation Matrix. V.E.1. Introductory Comments. V.E.2.The Two-State Case. V.E.3 The Three-State Case. V.E.4 The Multi-State Case. V.F. Quantization of the tau-Matrix and its Relation to the Size of Configuration Space: the Mathieu Equation as a Case of Study. IV.F.1. Derivation of the Eigenfunctions. IV.F.2. The non-Adiabatic Coupling Matrix and the Topological matrix. V.G Exercises. V.H. References. 6. The Molecular Field. VI.A. Solenoid as a Model for the Seam. VI.B. Two-State (Abelian) System. VI.B.1. The Non-Adiabatic Coupling Term as a Vector Potential. VI.B.2. Two-State Curl Equation. VI.B.3. The (Extended) Stokes Theorem. VI.B.4. Application of Stokes Theorem for several Conical Intersections. VI.B.5. Application of Vector-Algebra to Calculate the Field of a Two-State Hilbert Space. VI.B.6. A Numerical Example: The Study of the {Na,H2} System. VI. B.7. A Short Summary. VI.C. The Multi-State Hilbert Subspace. VI.C.1. The non-Abelian Stokes Theorem. VI.C.2. The Curl-Div Equations. VI.C.2.1. The Three-State Hilbert Subspace. VI.C.2.2. Derivation of the Poisson Equations. VI.C.2.3. The Strange Matrix Element and the Gauge Transformation. VI.D. A Numerical Study of the {H, H2} System. VI.D.1. Introductory Comments. VI.D.2. Introducing the Fourier Expansion. VI.D.3. Imposing Boundary Conditions. VI.D.4. Numerical Results. VI.E. The Multi-State Hilbert Subspace: On the Breakup of the Non-Adiabatic Coupling Matrix. VI.F. The Pseudo-Magnetic Field. VI.F.1. Quantization of the pseudo magnetic along the seam:. VI.F.2. The Non-Abelian Magnetic Fields. VI.G. Exercises: VI.H. References. 7. Open Phase and the Berry Phase for Molecular Systems. VII.A. Studies of Ab-initio Systems. VII.A.1. Introductory Comments. VII.A.2. The Open Phase and the Berry Phase for Single-valued Eigenfunctions ( Berry's Approach. VII.A.3. The Open Phase and the Berry Phase for Multi-valued Eigenfunctions ( the Present Approach. VII.A.3.1. Derivation of the Time-Dependent Equation. VII.A.3.2. The Treatment of the Adiabatic Case. VII.A.3.3. The Treatment of the non-Adiabatic (General) Case. VII.A.3.4. The {H2,H} System as a Case Study. VII.B. Phase-Modulus Relations for an External Cyclic Time-Dependent Field. VII.B.1. The Derivation of the Reciprocal Relations. VII.B.2. The Mathieu equation. VII.B.2.1. The Time-Dependent Schrodinger Equations. VII.B.2.2. Numerical Study of the Topological Phase. VII.B.3. Short Summary. VII.C. Exercises. VII.D. References. 8. Extended Born-Oppenheimer Approximations. VIII.A. Introductory Comments. VIII.B. The Born-Oppenheimer Approximation as Applied to a Multi-State Model-System. VIII.B.1. The Extended Approximate Born-Oppenheimer Equation. VIII.B.2. Gauge Invariance Condition for the Approximate Born-Oppenheimer Equation. VIII.C. Multi-State Born-Oppenheimer Approximation: Energy Considerations to Reduce the Dimension of the Diabatic Potential Matrix. VIII.C.1. Introductory Comments. VIII.C.2. Derivation of the Reduced Diabatic Potential Matrix. VIII.C.3. Application of the Extended Euler Matrix: Introducing the N-State Adiabatic-to-Diabatic Transformation Angle. VIII.C.3.1. Introductory Comments. VIII.C.3.2. Derivation of the Adiabatic-to-Diabatic Transformation Angle. VIII.C.4. Two-State Diabatic Potential Energy Matrix. VIII.C.4.1 Derivation of the Diabatic Potential Matrix. VIII.C.4.2 A Numerical Study of the (W-Matrix Elements. VIII.C.4.3 A Different Approach: The Helmholtz Decomposition. VIII.D. A Numerical Study of a Reactive Scattering Two-Coordinate Model. VIII.D.1. The Basic Equations. VIII.D.2. A Two-Coordinate Reactive (Exchange) Model. VIII.D.3. Numerical Results and Discussion. VIII.E. Exercises. VIII.F. References. 9. Summary. Index.

  • a quantum mechanical study of the reactive f H2 System a comparison between approximate jz exact and quasi classical cross sections
    Chemical Physics Letters, 1995
    Co-Authors: Efrat Rosenman, Sipora Hochmankowal, Avigdor Persky, Michael Baer
    Abstract:

    Abstract This work presents a quantum mechanical numerical study of the reactions F + H 2 ( v = 0, j = 0–4) → HF + H carried out on the T5A potential energy surface. The calculations were performed within the j z approximation and employed negative imaginary potentials, yielding state-selected cross sections and rate constants. The cross sections were compared with exact quantum mechanical and quasi-classical trajectory results and the rate constants were compared with experiment.

  • exact quantum mechanical three dimensional reactive probabilities for the d H2 System variational calculations based on negative imaginary absorbing potentials
    Chemical Physics Letters, 1992
    Co-Authors: Asher Baram, Michael Baer
    Abstract:

    Abstract We report on the first exact three-dimensional state-to-state reactive transition probabilities as obtained employing a variation (time independent) treatment based on negative imaginary absorbing potentials. The calculations were carried out for the D + H2(vj|J=0)→HD(v′j′|J=0) + H process. The results were found to fit reasonably well with those obtained by other methods.

Q A Zhang - One of the best experts on this subject based on the ideXlab platform.

  • a new reversible mg3ag H2 System for hydrogen storage
    Journal of Alloys and Compounds, 2013
    Co-Authors: T Z Si, Jian Zhang, Dong Liu, Q A Zhang
    Abstract:

    Abstract For the first time, the compound Mg 3 Ag was employed as a medium for hydrogen storage. It has been demonstrated that the hydriding/dehydriding process of Mg 3 Ag is reversible through the reaction Mg 3 Ag + 2H 2  ↔ 2MgH 2  + MgAg with obtaining altered thermodynamics. An enhanced cycling stability is also achieved by the capacity retention of 95% after 30 cycles, much higher than 70% for the pure Mg sample, which can be explained that the agglomeration and sintering of the resulting MgH 2 are efficiently prevented by the formation of hard and brittle MgAg phase upon multi-cycling.

  • comparative investigations on the hydrogenation characteristics and hydrogen storage kinetics of melt spun mg10nir r la nd and sm alloys
    International Journal of Hydrogen Energy, 2012
    Co-Authors: Q A Zhang, C J Jiang, D D Liu
    Abstract:

    Abstract The hydrogenation characteristics and hydrogen storage kinetics of the melt-spun Mg10NiR (R = La, Nd and Sm) alloys have been studied comparatively. It is found that the Mg10NiNd and Mg10NiSm alloys are in amorphous state but the Mg10NiLa alloy is composed of an amorphous phase and minor crystalline La2Mg17 after melt-spinning. The alloys can be hydrogenated into MgH2, Mg2NiH4 and a rare earth metal hydride RHx. The rare earth metal hydride and Mg2NiH4 synergistically provide a catalytic effect on the hydrogen absorption–desorption reactions in the Mg−H2 System. The hydrogen storage kinetics is not influenced by different rare earth metal hydrides but by the particle size of the rare earth metal hydrides.

Jacek Klos - One of the best experts on this subject based on the ideXlab platform.

  • quantum scattering of sis with H2 potential energy surface and rate coefficients at low temperature
    Journal of Chemical Physics, 2008
    Co-Authors: Francois Lique, Jacek Klos
    Abstract:

    Rotational excitation of the interstellar species SiS with H2 is investigated. We present a new four dimensional potential energy surface for the SiS–H2 System. Both molecules were treated as rigid rotors. Potential was obtained from the electronic structure calculations using a single- and double-excitation coupled cluster method with perturbative contributions from connected triple excitations [CCSD(T)]. The four atoms were described using the aug-cc-pVTZ basis sets. Bond functions were placed at mid-distance between the SiS center of mass and the center of mass of H2 for a better description of the van der Waals interaction. Additionally, at seven characteristic geometries, we calculated perturbational components of the interaction energy using symmetry-adapted perturbation theory approach to explain the anisotropy of the potential energy surface. Coupled-state calculations of the inelastic integral cross sections of SiS in collisions with para-H2 and ortho-H2 were calculated at low energies. After Bol...

  • ab initio potential energy and dipole moment surfaces infrared spectra and vibrational predissociation dynamics of the 35cl H2 d2 complexes
    Journal of Chemical Physics, 2003
    Co-Authors: Alexei A Buchachenko, Jacek Klos, T A Grinev, Evan J Bieske, M M Szczȩśniak, Grzegorz Chalasinski
    Abstract:

    Three-dimensional potential energy and dipole moment surfaces of the Cl−–H2 System are calculated ab initio by means of a coupled cluster method with single and double excitations and noniterative correction to triple excitations with augmented correlation consistent quadruple-zeta basis set supplemented with bond functions, and represented in analytical forms. Variational calculations of the energy levels up to the total angular momentum J=25 provide accurate estimations of the measured rotational spectroscopic constants of the ground van der Waals levels n=0 of the Cl−⋯H2/D2 complexes although they underestimate the red shifts of the mid-infrared spectra with v=0→v=1 vibrational excitation of the monomer. They also attest to the accuracy of effective radial interaction potentials extracted previously from experimental data using the rotational RKR procedure. Vibrational predissociation of the Cl−⋯H2/D2(v=1) complexes is shown to follow near-resonant vibrational-to-rotational energy transfer mechanism so...

Wan Azlina Wan Ab Karim Ghani - One of the best experts on this subject based on the ideXlab platform.

  • techno economic assessment of a novel integrated System of mechanical biological treatment and valorisation of residual municipal solid waste into hydrogen a case study in the uk
    Journal of Cleaner Production, 2021
    Co-Authors: Anh N Phan, Eleni Iacovidou, Wan Azlina Wan Ab Karim Ghani
    Abstract:

    Abstract Resources embedded in the waste streams are not properly recovered and most of them are ended up in landfills or only recovered as energy via energy-from-waste (EfW) facilities. Innovative resource recovery from waste strategies are urgently needed to maximise resource efficiency, divert waste from landfills and reduce reliance on EfW. This study proposes a novel mechanical-biological treatment with valorisation concept (MBT-v) which combines material recovery and fuel production, as alternatives to EfW for residual municipal solid waste (MSW) treatment. The polygeneration feature exhibited by the MBT-v System enhances resource efficiency and product diversification. The proposed MBT-v System involves valorisation of rejected materials from MBT into hydrogen by incorporating an additional gasification System. A comprehensive techno-economic assessment is conducted for the proposed MBT-v System and compared against a conventional MBT. The results reveal that the conventional MBT strongly relies on gate fees to be economically viable while it is heavily impacted by the rejects disposal cost. The analysis also shows that higher economic potential (36.4 M£/y) for MBT-v can be obtained compared to that of conventional MBT (3.4 M£/y) for a 100 kt/y residual MSW System. The minimum hydrogen selling price (MHSP) from the Gasification-H2 System is estimated to be at 3.4 £/kg (28.2 £/GJ), with potential for further reduction through upscaling the facility. This study concludes that producing high value product such as hydrogen (with the current assumed market price of hydrogen of 10 £/kg) can significantly improve the economic performance and minimise financial instability of the facilities. It is recommended that the scale and optimal configuration of MBT-v needs to be designed based on local conditions.

Francois Lique - One of the best experts on this subject based on the ideXlab platform.

  • quantum scattering of sis with H2 potential energy surface and rate coefficients at low temperature
    Journal of Chemical Physics, 2008
    Co-Authors: Francois Lique, Jacek Klos
    Abstract:

    Rotational excitation of the interstellar species SiS with H2 is investigated. We present a new four dimensional potential energy surface for the SiS–H2 System. Both molecules were treated as rigid rotors. Potential was obtained from the electronic structure calculations using a single- and double-excitation coupled cluster method with perturbative contributions from connected triple excitations [CCSD(T)]. The four atoms were described using the aug-cc-pVTZ basis sets. Bond functions were placed at mid-distance between the SiS center of mass and the center of mass of H2 for a better description of the van der Waals interaction. Additionally, at seven characteristic geometries, we calculated perturbational components of the interaction energy using symmetry-adapted perturbation theory approach to explain the anisotropy of the potential energy surface. Coupled-state calculations of the inelastic integral cross sections of SiS in collisions with para-H2 and ortho-H2 were calculated at low energies. After Bol...

  • rotationally inelastic collisions of so xσ 3 with H2 potential energy surface and rate coefficients for excitation by para H2 at low temperature
    Journal of Chemical Physics, 2007
    Co-Authors: Francois Lique, Maria Luisa Senent, A Spielfiedel, N Feautrier
    Abstract:

    Rotational excitation of the interstellar species SO(XΣ−3) with H2 is investigated. The authors present a new four-dimensional potential energy surface for the SO–H2 System, calculated at an internuclear SO distance frozen at its experimental minimum energy distance. It was obtained at the RCCSD(T) level using the aug-cc-pVTZ basis sets for the four atoms. Bond functions were placed at mid-distance between the SO center of mass and the center of mass of H2 for a better description of the van der Waals interaction. Close coupling calculations of the collisional excitation cross sections between the fine structure levels of SO by collisions with para-H2 are calculated at low energies which yield, after Boltzmann thermal average, rate coefficients up to 50K. The exact level splitting is taken into account. The propensity rules between fine structure levels are studied. It is shown that F-conserving cross sections are much larger, especially for high-N rotational levels, than F-changing cross sections, as fou...