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

Abstract

A novel valence bond based automatic diabatisation method by compression, called valence bond based compression approach for dibatization (VBCAD), is presented in this letter. It is a "blackbox" type method that provides an automatic diabatisation from a classical valence bond (VB) perspective. In VBCAD, a model space projection is performed by an eigenvalue decomposition algorithm followed by dimensional reduction based on a sequence of Householder transformations. Our diabaticity criterion is implemented in a way that maximizes the diversity of VB structure weights between different diabatic states. Owing to the rigorous Householder transformations employed in this entire procedure, the invariance of the target eigensubspace is preserved. This is illustrated on two prototypical examples.

A state-averaged orbital-optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states

“…In multistate quantum dynamics simulations, considering diabatic states is crucial to enforce smoothness of physical properties and to reduce the magnitude of non-adiabatic couplings, which explode around conical intersections or avoided crossings, signalling a break down of the Born-Oppenheimer approximation [81,119]. However, switching to a diabatic representation is not straightforward [120]. Hence, representing diabatic states like in figure 5(b) with SA-OO-VQE will allow the calculation of, for instance, smooth ground-and excited-state This diabatic representation in SA-OO-VQE needs to be assessed for more challenging systems, where more states could be required together with more complicated initial states.…”

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

“…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. 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.…”

“…This is how and why VBCAD makes plain use of the VB picture from a diabatic perspective. A more detailed exposition of VBCAD has been given 14 .…”

“…A more detailed exposition of VBCAD has been given. 14 In what follows, we present the proposed phase-correction in details. For a simple 2 × 2 real-symmetric Hamiltonian matrix in the diabatic representation i k j j j j j y…”

A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states

“…[49]), this is only possible properties and to reduce the magnitude of non-adiabatic couplings, which explode around conical intersections or avoided crossings, signaling a break down of the Born-Oppenheimer approximation [81,119]. However, switching to a diabatic representation is not straightforward [120]. Hence, representing diabatic states like in Fig.…”