Construction of Quasi-diabatic Hamiltonians That Accurately Represent ab Initio Determined Adiabatic Electronic States Coupled by Conical Intersections for Systems on the Order of 15 Atoms. Application to Cyclopentoxide Photoelectron Detachment in the Full 39 Degrees of Freedom

Abstract

We present, for systems of moderate dimension, a fitting framework to construct quasi-diabatic Hamiltonians that accurately represent ab initio adiabatic electronic structure data including the effects of conical intersections. The framework introduced here minimizes the difference between the fit prediction and the ab initio data obtained in the adiabatic representation, which is singular at a conical intersection seam. We define a general and flexible merit function to allow arbitrary representations and propose a representation to measure the fit–ab initio difference at geometries near electronic degeneracies. A fit Hamiltonian may behave poorly in insufficiently sampled regions, in which case a machine learning theory analysis of the fit representation suggests a regularization to address the deficiency. Our fitting framework including the regularization is used to construct the full 39-dimensional coupled diabatic potential energy surfaces for cyclopentoxy relevant to cyclopentoxide photoelectron detachment.

Machine Learning for Electronically Excited States of Molecules

“…For example, 356 data points were computed for the 15-atom cyclopentoxy molecule with MR-CISD(5,3)/cc-pVD(T)Z. 96 Respective calculations comprised 19,302,445 configuration state functions, and one reaction coordinate could be fitted in the diabatic basis. We also ran into a similar problem when fitting the excited states of the amino acid tyrosine containing 24 atoms, which also requires a multireference treatment.…”

“…Additionally, if certain reaction coordinates have been shown to be important in experiments or previous studies, then it is favorable to include data from scans along these reaction coordinates. 96 , 175 …”

Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing

“…(32) approximately, without the strict equality, to define quasi-diabatic states. [9][10][11][12][13][14][15][16][17] Approaches reviewed in this section form the traditional set of tools. The BO approximation is always made as the first step, with post-BO corrections introduced for more difficult cases.…”

“…While in general this cannot be done exactly, 8 there are procedures for defining approximate transformations. [9][10][11][12][13][14][15][16][17] The necessity for diabatization is a consequence of starting with the BO approximation.…”

Modeling Spin-Crossover Dynamics

“…NAMD, the same 10 6 electronic structure calculations will be required to build the global PESs and coupling surfaces for a system with 3 nuclear DOF, assuming the calculations generate a dense 3-dimensional grid with 100 points per each DOF. Modern surface interpolation techniques aimed to overcome the "curse of dimensionality" by using the sparse grids and focusing on the relevant parts of PESs can push the number of DOF to 24-39 (8-13 atoms), for roughly the same number of electronic structure calculations(97)(98)(99). Constructing the vibronic Hamiltonian models commonly used with the MCTDH method is less computationally expensive.…”