# Nonadiabatic coupling of the 1 1A″ and 2 1A″ states of ozone

01 May 1995-Vol. 194, Iss: 1, pp 45-64

TL;DR: In this article, the first-derivative nonadiabatic Born coupling terms for the two lowest-lying singlet A-excited states of ozone (1 A 2 and 1 B 1 in C 2v symmetry) whose electronic potential energy surfaces exhibit a crossing at a bond angle near 120° were derived.

Abstract: We report the results of ab initio calculations of the nonadiabatic Born coupling terms for the two lowest-lying singlet A″ excited states of ozone ( 1 A 2 and 1 B 1 in C 2v symmetry) whose electronic potential energy surfaces exhibit a crossing at a bond angle near 120°. Since photoexcitation from the ground state to these A″ states is believed to be responsible for the Chappuis band of ozone, determination of the nonadiabatic coupling terms in the molecular Hamiltonian is therefore likely to be of importance in understanding the predissociative features of the spectrum. The nuclear derivative coupling matrix elements are computed between ab initio electronic wavefunctions obtained from multi-reference configuration interaction (MRD-CI) calculations in a basis of configuration state functions constructed from MCSCF orbitals. The first-derivative nonadiabatic coupling terms are calculated analytically in a manner similar to the calculation of analytic energy gradients, thereby avoiding the cumbersome numerical differentiation of CI and SCF coefficients. The calculated analytical derivative coupling matrix elements are used to determine a suitable transformation to a quasidiabatic basis.

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TL;DR: In this article, the diabatization procedure of Atchity and Ruedenberg is extended to include more general types of crossings and avoided crossings of potential energy surfaces, which is more general than the previously proposed occupation number and natural orbital method, and remains valid even for chemical reactions that require multiple diabatic prototypes.

Abstract: In order to provide a practical framework for the calculation of diabatic (technically quasidiabatic) states, we generalize the diabatization procedures of Atchity and Ruedenberg to include more general types of crossings and avoided crossings of potential energy surfaces. The resulting diabatization procedure involves two steps: (i) the construction of diabatic orbitals and (ii) the construction of many-electron diabatic state functions in terms of the diabatic orbitals. The procedure for step (i) is more general than the previously proposed occupation number and natural orbital method, and the procedure for step (ii) remains valid even for chemical reactions that require multiple diabatic prototypes. The method is illustrated by applications to LiH, ozone, H2 dimer, and the reaction Li(2S,2P)+HF→LiF+H.

178 citations

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TL;DR: A time-dependent response approach to NACMEs which avoids explicit computation of excited-state wave functions is outlined and the Chernyak-Mukamel formula is shown to be equivalent to the Hellmann-Feynman contribution in analytical gradient theory.

Abstract: First-order nonadiabatic coupling matrix elements (NACMEs) are key for phenomena such as nonradiative transitions and excited-state decay, yet a consistent and practical first principles treatment has been elusive for molecules with more than a few heavy atoms. Here we present theory, implementation using Gaussian basis sets, and benchmarks of first-order NACMEs between ground and excited states in the framework of time-dependent hybrid density functional theory (TDDFT). A time-dependent response approach to NACMEs which avoids explicit computation of excited-state wave functions is outlined. In contrast to previous approaches, the present treatment produces exact analytical derivative couplings between time-dependent Kohn–Sham (TDKS) determinants in a finite atom-centered basis set. As in analytical gradient theory, derivative molecular orbital coefficients can be eliminated, making the computational cost independent of the number of nuclear degrees of freedom. Our expression reduces to the exact Chernya...

174 citations

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TL;DR: In this paper, the authors explore the relationship between symmetric and antisymmetric modes, concentrating on how this is modified by the presence of weak (e.g., environmentally or substitutionally induced) asymmetry.

Abstract: The most common methods used to describe the energy levels of charge-transfer systems (including mixed-valence systems) are the linear response approach of Rice and co-workers and the essentially equivalent PKS model described initially by Piepho, Krausz, and Schatz. While these methods were quite successful, in their original form they omitted the effects of overall symmetric vibrations. As a consequence, in particular they were not capable of adequately describing the electronic band width in the strong-coupling limit: Hush and later Ondrechen et al. demonstrated that symmetric modes are essential in this case, and modern versions of these models now include them. Here, we explore the relationship between symmetric and antisymmetric modes, concentrating on how this is modified by the presence of weak (e.g., environmentally or substitutionally induced) asymmetry. For the symmetric case, we show that when the electronic Hamiltonian operators are transformed from their usual localized diabatic representation into a delocalized diabatic representation, the effects of the symmetric and antisymmetric modes are interchanged. The primary effect of weak asymmetry is to mix the properties of the various modes, and possible consequences of this for the spectroscopy of bacterial photosynthetic reaction centre and substituted Creutz—Taube cations are discussed. We also consider the problem from an adiabatic Bom—Oppenheimer perspective and examine the regions in which this approach is appropriate.

89 citations

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TL;DR: Vibrationally averaged geometries, expectation values of rotational constants, and several adiabatic projection schemes developed in this work for tetratomic molecules are used to characterize the vibrational levels calculated by the DVR(6) and DVR (3) + DGB.

Abstract: We present two discrete variable representation (DVR) based methods for the determination of the vibrational energy levels of tetratomic molecules. Both methods are designed for orthogonal internal coordinates in a body-fixed reference frame and make use of the DVR of three angular variables. The angular DVRs allow the construction of a fixed-angle three-mode Hamiltonian for the stretching vibrations. For each of the angular triples, the stretching eigenvalue problems are solved by employing 3D radial DVRs in the DVR(6) approach and real three-dimensional distributed Gaussian functions in the DVR(3) + DGB method. The angular degrees of freedom are taken sequentially into account in conjunction with a contraction scheme resulting from several diagonalization/truncation steps. Vibrationally averaged geometries, expectation values of rotational constants, and several adiabatic projection schemes developed in this work for tetratomic molecules are used to characterize the vibrational levels calculated by the DVR(6) and DVR(3) + DGB.

57 citations

##### References

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01 Jan 1954

TL;DR: Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, and it remains the definitive treatment of the subject as mentioned in this paper. But it is not the most complete work on crystal lattice dynamics.

Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.

7,417 citations

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[...]

TL;DR: In this paper, the effects of contraction on the energies and one-electron properties of the water and nitrogen molecules were investigated, and the authors obtained principles which can be used to predict optimal contraction schemes for other systems without the necessity of such exhaustive calculations.

Abstract: The contraction of Gaussian basis functions for use in molecular calculations is investigated by considering the effects of contraction on the energies and one‐electron properties of the water and nitrogen molecules. The emphasis is on obtaining principles which can be used to predict optimal contraction schemes for other systems without the necessity of such exhaustive calculations. Using these principles, contractions are predicted for the first‐row atoms.

4,556 citations

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01 Jan 1977

TL;DR: In this paper, the authors present a method for determining configuration interaction wave functions for the Electronic States of Atoms and Molecules: the Vector Method, which is a general computer program for ab initio calculations.

Abstract: 1. Gaussian Basis Sets for Molecular Calculations.- 2. The Floating Spherical Gaussian Orbital Method.- 3. The Multiconfiguration Self-Consistent Field Method.- 4. The Self-Consistent Field Equations for Generalized Valence Bond and Open-Shell Hartree-Fock Wave Functions.- 5. Pair Correlation Theories.- 6. The Method of Configuration Interaction.- 7. The Direct Configuration Interaction Method from Molecular Integrals.- 8. A New Method for Determining Configuration Interaction Wave Functions for the Electronic States of Atoms and Molecules: The Vector Method.- 9. The Equations of Motion Method: An Approach to the Dynamical Properties of Atoms and Molecules.- 10. POLYATOM: A General Computer Program for Ab Initio Calculations.- 11. Configuration Expansion by Means of Pseudonatural Orbitals.- Author Index.

1,795 citations

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TL;DR: A new geometric phase factor is defined for any cyclic evolution of a quantum system, independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for a given projection of the evolution on the projective space of rays of the Hilbert space.

Abstract: A new geometric phase factor is defined for any cyclic evolution of a quantum system. This is independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for a given projection of the evolution on the projective space of rays of the Hilbert space. Some applications, including the Aharonov-Bohm effect, are considered. For the special case of adiabatic evolution, this phase factor is a gauge-invariant generalization of the one found by Berry.

1,665 citations

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TL;DR: In this article, it was shown that the geometrical phase factor found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle.

Abstract: It is shown that the "geometrical phase factor" recently found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem naturally defines a connection in such a bundle. This not only takes the mystery out of Berry's phase factor and provides calculational simple formulas, but makes a connection between Berry's work and that of Thouless et al. This connection allows the author to use Berry's ideas to interpret the integers of Thouless et al. in terms of eigenvalue degeneracies.

1,370 citations