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Adiabatic-diabatic representation

the electronic wavefunctions are taken as the eigenfunctions of the electronic Hamiltonian. In this case, all the coupling matrix elements H[j = ( // ff /y) are zero, and the coupling between different electronic states occurs through the nuclear kinetic energy terms this formulation is called the adiabatic representation.  [Pg.87]

Alternatively, a diabatic representation can be used. In this representation, the electronic wavefunctions used to expand the total wavefunction are not the eigenfunctions of the electronic Hamiltonian, but they are chosen so as to eliminate the derivative coupling. Therefore, the coupling terms do not appear in the Schrodinger equation, but the matrix element Hij = ( l 7 ff l y) is nonzero, which is the term responsible for the coupling of states. [Pg.87]

Note that [)/ are electronic wavefunctions that are not eigenfunctions of H. In every realistic case (except in diatomic molecules) where the sum over states J is truncated, the derivative coupling cannot vanish completely for every but it can become negligibly small. Making f/y very small corresponds to choosing the electronic wavefunctions so that they are always smooth functions of the nuclear coordinates. Physically diabatic functions maintain the character of the states. For example, assume that a diabatic state [)] corresponds to a covalent configuration and another diabatic state 2 corresponds to an ionic configuration. Before a nonadiabatic transition occurs, the adiabatic states will be the same, v /i = tj)/ and v(72 = 2. After a nonadiabatic [Pg.87]


Baer M 1975 Adiabatic and diabatic representations for atom-molecule collisions treatment of the collinear arrangement Chem. Rhys. Lett. 35 112... [Pg.2323]

Single surface calculations with a vector potential in the adiabatic representation and two surface calculations in the diabatic representation with or without shifting the conical intersection from the origin are performed using Cartesian coordinates. As in the asymptotic region the two coordinates of the model represent a translational and a vibrational mode, respectively, the initial wave function for the ground state can be represented as. [Pg.47]

It is important to note that the two surface calculations will be carried out in the diabatic representation. One can get the initial diabatic wave function matrix for the two surface calculations using the above adiabatic initial wave function by the following orthogonal transformation,... [Pg.47]

This makes it desirable to define other representations in addition to the electronically adiabatic one [Eqs. (9)-(12)], in which the adiabatic electronic wave function basis set used in the Bom-Huang expansion (12) is replaced by another basis set of functions of the electronic coordinates. Such a different electronic basis set can be chosen so as to minimize the above mentioned gradient term. This term can initially be neglected in the solution of the / -electionic-state nuclear motion Schrodinger equation and reintroduced later using perturbative or other methods, if desired. This new basis set of electronic wave functions can also be made to depend parametrically, like their adiabatic counterparts, on the internal nuclear coordinates q that were defined after Eq. (8). This new electronic basis set is henceforth refened to as diabatic and, as is obvious, leads to an electronically diabatic representation that is not unique unlike the adiabatic one, which is unique by definition. [Pg.188]

U(qJ is referred to as an adiabatic-to-diabatic transformation (ADT) matrix. Its mathematical sbucture is discussed in detail in Section in.C. If the electronic wave functions in the adiabatic and diabatic representations are chosen to be real, as is normally the case, U(q ) is orthogonal and therefore has n n — l)/2 independent elements (or degrees of freedom). This transformation mabix U(qO can be chosen so as to yield a diabatic electronic basis set with desired properties, which can then be used to derive the diabatic nuclear motion Schrodinger equation. By using Eqs. (27) and (28) and the orthonormality of the diabatic and adiabatic electronic basis sets, we can relate the adiabatic and diabatic nuclear wave functions through the same n-dimensional unitary transformation matrix U(qx) according to... [Pg.189]

In the two-adiabatic-electronic-state Bom-Huang description of the total orbital wave function, we wish to solve the corresponding nuclear motion Schrodinger equation in the diabatic representation... [Pg.208]

The adiabatic picture is the standard one in quantum chemistry for the reason that, not only is it mathematically well defined, but it is also that used in ab initio calculations, which solve the electronic Hamiltonian at a particular nuclear geometry. To see the effects of vibronic coupling on the potential energy surfaces one must move to what is called a diabatic representation [1,65,180, 181]. [Pg.279]

In a diabatic representation, the electronic wave functions are no longer eigenfunctions of the electronic Hamiltonian. The aim is instead that the functions are so chosen that the (nonlocal) non-adiabatic coupling operator matrix, A in Eq. (52), vanishes, and the couplings are represented by (local) potential operators. The nuclear Schrddinger equation is then written... [Pg.279]

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... [Pg.584]

There are three ways of implementing the GP boundary condition. These are (1) to expand the wave function in terms of basis functions that themselves satisfy the GP boundary condition [16] (2) to use the vector-potential approach of Mead and Truhlar [6,64] and (3) to convert to an approximately diabatic representation [3, 52, 65, 66], where the effect of the GP is included exactly through the adiabatic-diabatic mixing angle. Of these, (1) is probably the most... [Pg.18]

In the previous section, we discussed the calculation of the PESs needed in Eq. (2.16a) as well as the nonadiabatic coupling terms of Eqs. (2.16b) and (2.16c). We have noted that in the diabatic representation the off-diagonal elements of Eq. (2.16a) are responsible for the coupling between electronic states while Dp and Gp vanish. In the adiabatic representation the opposite is true The off-diagonal elements of Eq. (2.16a) vanish while Du and Gp do not. In this representation, our calculation of the nonadiabatic coupling is approximate because we assume that Gp is negligible and we make an approximation in the calculation of Dp. (See end of Section n.A for more details.)... [Pg.449]

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... [Pg.74]

We have used the above analysis scheme for all single- and two-surface calculations. Thus, when the wave function is represented in polar coordinates, we have mapped the wave function, 4,ad(, t) to Tatime step to use in Eq. (17) and as the two surface calculations are performed in the diabatic representation, the wave function matrix is back transformed to the adiabatic representation in each time step as... [Pg.154]


See other pages where Adiabatic-diabatic representation is mentioned: [Pg.87]    [Pg.87]    [Pg.50]    [Pg.87]    [Pg.181]    [Pg.215]    [Pg.280]    [Pg.280]    [Pg.769]    [Pg.99]    [Pg.444]    [Pg.468]    [Pg.496]    [Pg.497]    [Pg.61]    [Pg.71]    [Pg.71]    [Pg.75]    [Pg.93]    [Pg.96]    [Pg.185]    [Pg.191]    [Pg.285]    [Pg.319]    [Pg.385]   
See also in sourсe #XX -- [ Pg.87 ]




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