Two-Dimensional Analysis of the Diabatic Transition of a General Vectorial Physical Observable Based on Adiabatic-to-Diabatic Transformation

Abstract

We present a full analysis of the magnitude and orientation of the diabatic transition matrix element of a general vectorial physical observable during the adiabatic-to-diabatic transformation. The diabatic transition is a function of the adiabatic-to-diabatic transformation angle and the two basic vectors of the adiabatic states, which are the off-diagonal matrix element and the difference between the two diagonal matrix elements. To the best of our knowledge, this is the first time that the transformation has been accomplished in a more general two-dimensional scale for a vectorial physical observable. All possible extreme values of a diabatic transition are deduced for systems with different features. By using an approximate diabatic transition dipole, the pilot implementation of the analysis produces an electronic coupling curve nearly identical to that obtained by the generalized Mulliken–Hush method for the testing molecule. Evidently, this complete analysis of a diabatic transition will be very useful in determining the adiabatic-to-diabatic transformation angle by using a physical observable and can also be used to evaluate the quality of various approximations for constructing the diabatic states.

Anti-Electrostatic Main Group Metal–Metal Bonds That Activate CO2

“…The BLW computations at the same M06-2X-D3/6-311++G­(d,p) theoretical level, , however, were carried out with GAMESS to which our BLW code was ported in our laboratories. The BLW method is a variant of ab initio valence bond (VB) theory − and can derive electron strictly localized states (i.e., Lewis states) self-consistently. On the basis of the BLW method, the intermolecular binding energy can be decomposed to the sum of deformation energy (Δ E def ), frozen energy (Δ E F ), polarization (Δ E pol ), charge transfer (Δ E CT ), and dispersion correction (δE disp ) components. , For a complex AB composed of interacting moieties A and B, the binding energy (Δ E b ) corresponding to the energy change from optimal monomers A and B to the optimal complex AB is where BSSE is the basis set superposition error evaluated by the Boys–Bernardi counterpoise method .…”

Diabatization around Conical Intersections with a New Phase-Corrected Valence-Bond-Based Compression Approach

“…In addition, if a global diabatic representation were known, we could circumvent the heavy task of calculating such couplings around conical intersections; unfortunately, such a representation is not available directly and must be constructed with some diabatization scheme, which relies on the choice of a diabatic criterion. Among them, ab initio diabatization approaches are based on the properties of adiabatic electronic wave functions in terms of configurations [1][2][3][4][5][6][7][8][9][10][11][12][13] . Recently, a valence-bond-based compression approach for diabatization (VBCAD) has been proposed 14 ; it allows a low-size diabatic Hamiltonian matrix to be built automatically.…”

“…In addition, if a global diabatic representation were known, we could circumvent the heavy task of calculating such couplings around conical intersections; unfortunately, such a representation is not available directly and must be constructed with some diabatization scheme, which relies on the choice of a diabatic criterion. Among them, ab initio diabatization approaches are based on the properties of adiabatic electronic wave functions in terms of configurations. − Recently, a valence-bond-based compression approach for diabatization (VBCAD) has been proposed; it allows a low-size diabatic Hamiltonian matrix to be built automatically. The central idea is to reduce, i.e., compress, the full electronic Hamiltonian matrix upon employing a series of Householder transformations coupled to a VB-based diabatization criterion, which take explicit advantage of Lewis VB structures with specific bonding patterns.…”

A Novel Valence-Bond-Based Automatic Diabatization Method by Compression

“…Therefore, some alternative strategies have been proposed over the years, based on the properties of the adiabatic wave functions, whereby the adiabatic-to-diabatic (ATD) transformation is defined in order to enforce the smoothness of physical properties [5][6][7][8][9] , or of the expressions of the electronic wave functions in terms of configurations [10][11][12][13][14][15][16] . As large non-adiabatic couplings are related to fast changes of the adiabatic wave functions with respect to the nuclear coordinates, the key of these strategies is to construct the ATD transformation from its ability to reduce the changes.…”

“…In principle, the construction of approximate diabatic states is not unique. The direct way that stems from their formal definition requires the determination of all derivative couplings over an extended range of nuclear coordinates, which involves large computational effort. − Therefore, some alternative strategies have been proposed over the years, based on the properties of the adiabatic wave functions, whereby the adiabatic-to-diabatic (ATD) transformation is defined in order to enforce the smoothness of physical properties − or of the expressions of the electronic wave functions in terms of configurations. − As large nonadiabatic couplings are related to fast changes of the adiabatic wave functions with respect to the nuclear coordinates, the key to these strategies is to construct the ATD transformation from its ability to reduce the changes. In particular, the diabatic states can be obtained from the concept of block-diagonalization of the Hamiltonian, − which can be derived from a least-action principle.…”