Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities

Target State Optimized Density Functional Theory for Electronic Excited and Diabatic States

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.

Mechanism and Kinetics of Methane Combustion. Part II: Potential Energy Surface for Hydrogen-Abstraction Reaction of CH4 + O(3P)

Methane combustion plays an important role in various fields such as combustion chemistry and atmospheric chemistry of the stratosphere. Highly accurate study of its initial reaction remains a key challenge. Here, through extensive studies with a state-of-the-art ab initio and neural network method, we present a potential energy surface of the O(³P) + CH₄ → OH + CH₃ reaction on the ground state 1³A and the first excited state 2³A. In this work, the energies of 10 167 points covering all important regions are obtained with state-averaged complete active space self-consistent field calculations and then fitted using the Levenberg-Marquardt algorithm with a root-mean-square error of 0.391 and 0.442 kcal/mol for the 1³A and 2³A states, respectively. This study explores the characteristics of the radical van der Waals (VdW) complex and reveals a detailed mechanism of the methane combustion initial reaction. Within the scope of this mechanism, this surface gives a fairly accurate description of the regions around the saddle point, conical intersection, and vdW wells in the entrance for efficient computational simulations. As a theoretical study on a prototypical polyatomic reaction, it is hopeful that this work will modify our understanding of the primary process in hydrocarbon combustion.

Block-Localized Excitation for Excimer Complex and Diabatic Coupling

We describe a block-localized excitation (BLE) method to carry out constrained optimization of block-localized orbitals for constructing valence bond-like, diabatic excited configurations using multistate density functional theory (MSDFT). The method is an extension of the previous block-localized wave function method through a fragment-based ΔSCF approach to optimize excited determinants within a molecular complex. In BLE, both the number of electrons and the electronic spin of different fragments in a whole system can be constrained, whereas electrostatic, exchange, and polarization interactions among different blocks can be fully taken into account of. To avoid optimization collapse to unwanted states, a ΔSCF projection scheme and a maximum overlap of wave function approach have been presented. The method is illustrated by the excimer complex of two naphthalene molecules. With a minimum of eight spin-adapted configurational state functions, it was found that the inversion of L_a^- and L_b^- states near the optimal structure of the excimer complex is correctly produced, which is in quantitative agreement with DMRG-CASPT2 calculations and experiments. Trends in the computed transfer integrals associated with excited-state energy transfer both in the singlet and triplet states are discussed. The results suggest that MSDFT may be used as an efficient approach to treat intermolecular interactions in excited states with a minimal active space (MAS) for interpretation of the results and for dynamic simulations, although the selection of a small active space is often system dependent.

Accurate Neural Network Representation of the Ab Initio Determined Spin-Orbit Interaction in the Diabatic Representation Including the Effects of Conical Intersections

A method for fitting ab initio determined spin-orbit coupling interactions, in the Breit-Pauli approximation, based on quasidiabatic representations using neural network fits is reported. The algorithm generalizes our recently reported neural network approach for representing the dipole interaction. The S₀, S₁, and T₁ states of formaldehyde are used as an example. First, the two singlet states S₀ and S₁ are diabatized with a modified Boys Localization diabatization method. Second, the spin-orbit coupling between singlet and triplet states is transformed to the diabatic representation. This removes the discontinuities in the adiabatic representation. The diabatized spin-orbit couplings are then fit with smooth neural network functions. The analytic representation of spin-orbit coupling interactions in a diabatic basis by neural networks will make accurate full-dimensional quantum dynamical treatment of both internal conversion and intersystem crossing possible, which will help us to gain better understanding of both processes.

Determining whether diabolical singularities limit the accuracy of molecular property based diabatic representations: The 1,21A states of methylamine

An efficient, easily implemented method for locating singularities attributable to the failure of the defining equations in a molecular property based diabatization, termed diabolical singular points, is reported. For two state diabatizations, the singular points form a seam of dimension N ^int - 2, where N ^int is the number of internal degrees of freedom. The dynamical outcomes of nuclear trajectories that reach the region of this seam are flawed. The algorithm easily identifies these otherwise hard to anticipate regions of fallaciously large derivative coupling. The fact that the algorithm is easily incorporated into a two state diabatization code based on molecular properties makes it a practical tool for determining whether the existence of diabolical singularities is relevant to the problem being considered. The algorithm is illustrated using a multireference single and double excitation configuration interaction description of the 1,2¹A states of CH₃NH_2.

Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition

A procedure, called generalized diabatic-at-construction (GDAC), is presented to transform adiabatic potential energy surfaces into a diabatic representation by generalized singular value decomposition. First, we use a set of localized, valence bond-like configuration state functions, called DAC, as the basis states. Then, the adiabatic ground and relevant excited states are determined using multistate density functional theory (MSDFT). GDAC differs in the opposite direction from traditional approaches based on adiabatic-to-diabatic transformation with certain property restraints. The method is illustrated with applications to a model first-order bond dissociation reaction of CH₃OCH₂Cl polarized by a solvent molecule, the ground- and first-excited-state potential energy surfaces near the minimum conical intersection for the ammonia dimer photodissociation, and the multiple avoided curve crossings in the dissociation of lithium hydride. The GDAC diabatization method may be useful for defining charge-localized states in studies of electron transfer and proton-coupled electron transfer reactions in proteins.

Direct diabatization based on nonadiabatic couplings: the N/D method

We propose a new diabatization method that is direct, orbital-free, and adiabatic-equivalent based on directly calculated nonadiabatic couplings of states and the adiabatic energy gradients.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Accurate nonadiabatic dynamics

This Perspective addresses the use of coupled diabatic potential energy surfaces (PESs) together with rigorous quantum dynamics in full or reduced dimensional coordinate spaces to obtain accurate solutions to problems in nonadiabatic dynamics.