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State adiabatic

Solution of this set for F R) represents tire adiabatic close-coupling method. The adiabatic states are nomrally detennined (via standard computational teclmiques of quanUim chemistry) relative to a set of axes (X, Y, Z ) with the Z- axis directed along the nuclear separation R. On transfomring to this set which rotates during the collision, then /(r, / ), for the diatomic A-B case, satisfies... [Pg.2042]

The non-adiabatic effect on the ground adiabatic state dynamics can as mentioned in the introduction be incorporated either by including a vector potential... [Pg.44]

We present state-to-state transition probabilities on the ground adiabatic state where calculations were performed by using the extended BO equation for the N = 3 case and a time-dependent wave-packet approach. We have already discussed this approach in the N = 2 case. Here, we have shown results at four energies and all of them are far below the point of Cl, that is, E = 3.0 eV. [Pg.71]

In this chapter, we discussed the significance of the GP effect in chemical reactions, that is, the influence of the upper electronic state(s) on the reactive and nonreactive transition probabilities of the ground adiabatic state. In order to include this effect, the ordinary BO equations are extended either by using a HLH phase or by deriving them from first principles. Considering the HLH phase due to the presence of a conical intersection between the ground and the first excited state, the general fomi of the vector potential, hence the effective... [Pg.79]

As already mentioned, the results in Section HI are based on dispersions relations in the complex time domain. A complex time is not a new concept. It features in wave optics [28] for complex analytic signals (which is an electromagnetic field with only positive frequencies) and in nondemolition measurements performed on photons [41]. For transitions between adiabatic states (which is also discussed in this chapter), it was previously intioduced in several works [42-45]. [Pg.97]

Interestingly, the need for a multiple electronic set, which we connect with the reciprocal relations, was also a keynote of a recent review ([46] and previous publications cited there and in [47]). Though the considerations relevant to this effect are not linked to the complex nature of the states (but rather to the stability of the adiabatic states in the real domain), we have included in Section HI a mention of, and some elaboration on, this topic. [Pg.97]

As shown in Eq. (92), the gauge field aJ is simply related to the non-adiabatic coupling elements For an infinite set of electtonic adiabatic states [A = 00 in Eq. (90)], Ftc = 0. This important results seems to have been first established... [Pg.157]

This diabatization matrix only mixes the adiabatic states 2 and 4 leaving the states 1 and 3 unchanged. [Pg.192]

Obviously, the BO or the adiabatic states only serve as a basis, albeit a useful basis if they are determined accurately, for such evolving states, and one may ask whether another, less costly, basis could be Just as useful. The electron nuclear dynamics (END) theory [1-4] treats the simultaneous dynamics of electrons and nuclei and may be characterized as a time-dependent, fully nonadiabatic approach to direct dynamics. The END equations that approximate the time-dependent Schrddinger equation are derived by employing the time-dependent variational principle (TDVP). [Pg.221]

The superaiatrix notation emphasizes the structure of the problem. Each diagonal operator drives a wavepaclcet, just as in the adiabatic case of Eq. (10), but here the motion of the wavepackets in different adiabatic states is mixed by the off-diagonal non-adiabatic operators. In practice, a single matrix is built for the operator, and a single vector for the wavepacket. The operator matrix elements in the basis set <() are... [Pg.279]

The motivation comes from the early work of Landau [208], Zener [209], and Stueckelberg [210]. The Landau-Zener model is for a classical particle moving on two coupled ID PES. If the diabatic states cross so that the energy gap is linear with time, and the velocity of the particle is constant through the non-adiabatic region, then the probability of changing adiabatic states is... [Pg.292]

While this derivation uses a complete set of adiabatic states, it has been shown [54] that this equation is also valid in a subset of mutually coupled states that do not interact with the other states. [Pg.314]

Appendix D Degenerate and Near-Degenerate Vibrational Levels Appendix E Adiabatic States in the Vicinity of a Conical Intersection 1, Jahn-Teller Theorem... [Pg.552]

APPENDIX E ADIABATIC STATES IN THE VICINITY OF A CONICAL INTERSECTION... [Pg.625]

We follow Thompson and Mead [13] to discuss the behavior of the electronic Hamiltonian, potential energy, and derivative coupling between adiabatic states in the vicinity of the D31, conical intersection. Let A be an operator that transforms only the nuclear coordinates, and A be one that acts on the electronic degrees of freedom alone. Clearly, the electronic Hamiltonian satisfies... [Pg.627]

At this point, we make two comments (a) Conditions (1) and (2) lead to a well-defined sub-Hilbert space that for any further treatments (in spectroscopy or scattering processes) has to be treated as a whole (and not on a state by state level), (b) Since all states in a given sub-Hilbert space are adiabatic states, stiong interactions of the Landau-Zener type can occur between two consecutive states only. However, Demkov-type interactions may exist between any two states. [Pg.664]


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Adiabatic approach states

Adiabatic change of state

Adiabatic conditions, steady-state

Adiabatic conditions, steady-state equations

Adiabatic electronic state

Adiabatic excited state

Adiabatic exciton states

Adiabatic ground state

Adiabatic ground state potential

Adiabatic path single excited state

Adiabatic photoreactions ground state

Adiabatic representation electronic states

Adiabatic state representation

Adiabatic state representation trajectory surface hopping

Adiabatic states infinite number

Adiabatic states, splitting

Adiabatic transition state theory

Adiabatic-to-diabatic transformation two-state application

Anti-adiabatic state

Born-Oppenheimer electronic states adiabatic

Bound-state dynamics, adiabatic

Bound-state dynamics, adiabatic approximation

Classical mechanics adiabatic states

Coherent states stimulated Raman adiabatic passage

Coupling matrices, electronic state adiabatic

Coupling matrices, electronic state adiabatic representation

Coupling states intramolecular dynamics, adiabatic

Diabatic and adiabatic states

Electronic state adiabatic representation Born-Huang expansion

Electronic states, adiabatic-to-diabatic

Electronic states, adiabatic-to-diabatic transformation, two-state system

Four-state molecular system, non-adiabatic

Generalization of the adiabatic electronic states

Geometric phase effect adiabatic states, conical intersections

Jahn-Teller effect conical intersection, adiabatic state

Molecular potential adiabatic states

Multiple steady states in an adiabatic CSTR

Non-adiabatic coupling three-state matrix quantization

Non-adiabatic coupling three-state system analysis

Non-adiabatic coupling two-state molecular system

Non-adiabatic coupling, two-state molecular

Nuclear dynamics adiabatic states, conical intersections

Permutational symmetry adiabatic states, conical intersections

Permutational symmetry, adiabatic states

Predissociation for a pair of states intermediate between adiabatic and diabatic coupling limits

Quantum reaction dynamics, electronic states adiabatic representation

Quasi-adiabatic states

SCSAC adiabatic ground state

Semiclassical adiabatic ground-state

Semiclassical adiabatic ground-state dynamics

Single-valued adiabatic state

Single-valued adiabatic state matrix

State space reversible adiabat

Three-state molecular system, non-adiabatic

Three-state molecular system, non-adiabatic extended Born-Oppenheimer equations

Three-state molecular system, non-adiabatic minimal diabatic potential matrix

Three-state molecular system, non-adiabatic noninteracting conical intersections

Three-state molecular system, non-adiabatic numerical study

Three-state molecular system, non-adiabatic quantization

Three-state molecular system, non-adiabatic sign flip derivation

Three-state molecular system, non-adiabatic strongly coupled conical

Three-state molecular system, non-adiabatic theoretical-numeric approach

Three-state molecular system, non-adiabatic transformation matrices

Transition State Geometric Structure in the Adiabatic PT Picture

Transition state vibrationally adiabatic

Two-state molecular system, non-adiabatic

Two-state molecular system, non-adiabatic C2H-molecule: conical

Two-state molecular system, non-adiabatic Herzberg-Longuet-Higgins phase

Two-state molecular system, non-adiabatic intersections

Two-state molecular system, non-adiabatic quantization

Two-state molecular system, non-adiabatic single conical intersection solution

Two-state molecular system, non-adiabatic systems

Two-state molecular system, non-adiabatic transformation matrices

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