Dressed adiabatic and diabatic potentials to study conical intersections for F + H2.
TL;DR: According to this study, the most one should expect, in case of F + H(2), is a mild effect of the (1, 2) ci on its reactive/exchange process--an outcome also supported by experiment.
Abstract: We follow a suggestion by Lipoff and Herschbach [Mol. Phys. 108, 1133 (2010)10.1080/00268971003662912] and compare dressed and bare adiabatic potentials to get insight regarding the low-energy dynamics (e.g., cold reaction) taking place in molecular systems. In this particular case, we are interested to study the effect of conical intersections (ci) on the interacting atoms. For this purpose, we consider vibrational dressed adiabatic and vibrational dressed diabatic potentials in the entrance channel of reactive systems. According to our study, the most one should expect, in case of F + H2, is a mild effect of the (1, 2) ci on its reactive/exchange process−an outcome also supported by experiment. This happens although the corresponding dressed and bare potential barriers (and the corresponding van der Waals potential wells) differ significantly from each other.
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TL;DR: In this article, the development on beyond Born-Oppenheimer (BBO) theory and its implementation on various models and realistic molecular processes as carried out over the last 15 years are reviewed.
Abstract: We review our development on beyond Born–Oppenheimer (BBO) theory and its implementation on various models and realistic molecular processes as carried out over the last 15 years. The theoretical f...
33 citations
01 May 2010
TL;DR: The basic principles that define the diabatic basis are summarized and it is demonstrated how they can be applied in the specific context of constrained density functional theory.
Abstract: Diabatic states have a long history in chemistry, beginning with early valence bond pictures of molecular bonding and extending through the construction of model potential energy surfaces to the modern proliferation of methods for computing these elusive states. In this review, we summarize the basic principles that define the diabatic basis and demonstrate how they can be applied in the specific context of constrained density functional theory. Using illustrative examples from electron transfer and chemical reactions, we show how the diabatic picture can be used to extract qualitative insight and quantitative predictions about energy landscapes. The review closes with a brief summary of the challenges and prospects for the further application of diabatic states in chemistry.
30 citations
TL;DR: The question whether a Berry phase should be included in the calculation of rovibronic states of the ozone molecule in its electronic ground state has been addressed in the present work.
Abstract: The question whether a Berry phase should be included in the calculation of rovibronic states of the ozone molecule in its electronic ground state has been addressed in the present work. Since seve...
18 citations
TL;DR: The present study is characterized by planar contours that intersect the collinear axis, thus, forming a unique type of RT-non-adiabatic coupling terms (NACT) expressed in terms of Dirac-δ functions, and reveals an unexpected result of the following kind.
Abstract: The present study concentrates on a situation where a Renner-Teller (RT) system is entangled with Jahn-Teller (JT) conical intersections. Studies of this type were performed in the past for contours that surround the RT seam located along the collinear axis [see, for instance, G. J. Halasz, A. Vibok, R. Baer, and M. Baer, J. Chem. Phys. 125, 094102 (2006)]. The present study is characterized by planar contours that intersect the collinear axis, thus, forming a unique type of RT-non-adiabatic coupling terms (NACT) expressed in terms of Dirac-δ functions. Consequently, to calculate the required adiabatic-to-diabatic (mixing) angles, a new approach is developed. During this study we revealed the existence of a novel molecular parameter, η, which yields the coupling between the RT and the JT NACTs. This parameter was found to be a pure number η = 22/π (and therefore independent of any particular molecular system) and is designated as Renner-Jahn coupling parameter. The present study also reveals an unexpected result of the following kind: It is well known that each (complete) group of states, responsible for either the JT-effect or the RT-effect, forms a Hilbert space of its own. However, the entanglement between these two effects forms a third effect, namely, the RT/JT effect and the states that take part in it form a different Hilbert space.
18 citations
TL;DR: This study investigates the effect of chemical substituents on the functional properties of a molecular photoswitch by means of theoretical tools, revealing the fulfillment of several molecular switch properties of the studied quinoline compounds.
Abstract: This study investigates the effect of chemical substituents on the functional properties of a molecular photoswitch (Phys. Chem. Chem. Phys., 2008, 10, 1243) by means of theoretical tools. Molecular switches are known to consist of so-called frame and crane components. Several functional groups are substituted to the 7-hydroxyquinoline molecular frame at position 8 as crane fragments. The impact of π-electron donating NH2 groups attached to the frame is also investigated. Excited state intramolecular hydrogen transfer mediated by the frame-crane torsion has been considered as a possible reaction mechanism. For all the investigated systems, we present the resulting potential energy profiles of the ground and first excited states. Vertical excitation energies and oscillator strengths of the 5 lowest-lying excited electronic states calculated at the two terminal points of the reaction path are also presented. Single point calculations were carried out at the CC2 level, while the presence of conical intersections between the ground and first excited states near perpendicular twisted geometries was demonstrated using the CASSCF method. Our results undoubtedly reveal the fulfillment of several molecular switch properties of the studied quinoline compounds. Comparisons between the different substituted systems have also been made.
13 citations
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TL;DR: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird as discussed by the authors.
Abstract: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird. Mehratomige Molekeln werden in entsprechender Weise als starre „Kreisel“ angesehen.2) Dieser Standpunkt erlaubt es, die einfachsten Gesetze der Bandenspektren und der spezifischen Warme mehratomiger Gase zu erklaren. Das nachste Stadium1) last die Annahme starrer Verbindungen zwischen den Atomen fallen und berucksichtigt die Kernschwingungen, zunachst als harmonische Schwingungen; dabie ergenben sich nach Sponer3) und Kratzer4) Zusammenhange zwischen den einzelnen Banden eines Bandensystems.
4,131 citations
TL;DR: In this article, a contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation, and second-order perturbation theory overestimated the correlated energy by 23-50% depending on how H0 was chosen.
Abstract: A contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation. Second-order perturbation theory overestimated the correlation energy by 23–50% depending on how H0 was chosen. Pair-pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.
2,374 citations
28 Mar 2006
TL;DR: In this paper, the authors present an analysis of the non-Abelian case of the Adiabatic transformation matrix in terms of time dependent and non-abelian components.
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.
482 citations
TL;DR: In this paper, some aspects of the atom-molecule interactions are extended to include electronic transitions and the main emphasis is directed towards the close relationship between the adiabatic and the diabatic representations.
405 citations
TL;DR: In this article, a three dimensional potential energy surface for the F+H2→HF+H reaction has been computed using the internally contracted multireference configuration interaction (MRCI) method with complete active space self-consistent field (CASSCF) reference functions and a very large basis set.
Abstract: A three dimensional potential energy surface for the F+H2→HF+H reaction has been computed using the internally contracted multireference configuration interaction (MRCI) method with complete active space self‐consistent field (CASSCF) reference functions and a very large basis set. Calibration calculations have been performed using the triple‐zeta plus polarization basis set employed in previous nine‐electron full CI (FCI) calculations of Knowles, Stark, and Werner [Chem. Phys. Lett. 185, 555 (1991)]. While all variational MRCI wave functions yield considerably larger barrier heights than the FCI, excellent agreement with the FCI barrier height and the exothermicity was obtained when the Davidson correction was applied (MRCI+Q). The convergence of the barrier height and exothermicity, spectroscopic constants of the HF and H2 fragments, and the electron affinity of the fluorine atom with respect to the basis set has been carefully tested. Using the largest basis sets, which included 5d, 4f, 3g, and 2h func...
376 citations