The electron-propagator approach to conceptual density-functional theory

Does the radical GPRI strongly depend on the population scheme? A comparative study to predict radical attack on unsaturated molecules with the radical general-purpose reactivity indicator

The reactivity of 22 unsaturated molecules undergoing attack by a methyl radical (⋅CH3) have been elucidated using the condensed radical general-purpose reactivity indicator (condensed radical GPRI) appropriate for relatively nucleophilic or electrophilic molecules. Using the appropriate radical GPRI equation for electrophilic attack or nucleophilic radical attack, seven different population schemes were used to assign the most reactive atoms in each of the 22 molecules. The results show that the condensed radical GPRI is sensitive to the population scheme chosen, but less sensitive than the radical Fukui function. Therefore, the reliability of these methods depends on the population scheme. Our investigation indicates that the condensed radical GPRI is most accurate in predicting the dominant products of the methyl radical addition reactions on a variety of unsaturated molecules when the Hirshfeld, Merz-Singh-Kollman, or Voronoi deformation density population schemes are used. Furthermore, for all populations schemes in the majority of instances where the radical Fukui function failed the radical GPRI was able to identify the most reactive atom under certain reactivity conditions.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Koopmans’ multiconfigurational self-consistent field (MCSCF) Fukui functions and MCSCF perturbation theory

Prediction of chemical reactivity has become one of the highest priority tasks of computational chemistry since the development of the methods of modeling electronic structure. Despite the general simplicity of the physical concept of reactivity and the rapid development of modern density functional theory (DFT) methods, this task remains state-of-the-art for systems with wavefunctions that have a multiconfigurational character. In such cases, for the accurate description of reactivity one needs to use multiconfigurational approaches that are much heavier computationally then ordinary single-determinant DFT methods. Moreover, the complexity of the calculation of reactivity is increased by the necessity to calculate ionic and transition states. These computational challenges can be addressed by employing the concepts of Koopmans’ theorem and its extension to a multiconfigurational case. We present a simplified methodology for the calculation of Fukui functions, based on Koopmans’ approximation for multiconfigurational Green’s functions developed in our previous works. Also, an extension of this methodology based on perturbation theory has been developed to improve accuracy.

Stability conditions for density functional reactivity theory: an interpretation of the total local hardness

The second-order Taylor series expansions commonly used in the density functional chemical reactivity theory are used to define local stability conditions for electronic states. Systems which satisfy these conditions are stable to infinitesimal perturbations due to approaching chemical reagents. The basic formalism considered here supersedes previous variational approaches to chemical reactivity theory like the electrophilicity, potentialphilicity, and chargephilicity. The total local hardness emerges naturally in this analysis, and can be clearly interpreted. When the total local hardness is small, the system is relatively insensitive to perturbations. Furthermore, minus the total local hardness is an energetically favorable perturbation of the external potential.

Removing Electrons Can Increase the Electron Density: A Computational Study of Negative Fukui Functions

Ab initio and density-functional theory calculations for a family of substituted acetylenes show that removing electrons from these molecules causes the electron density along the C-C bond to increase. This result contradicts the predictions of simple frontier molecular orbital theory, but it is easily explained using the nucleophilic Fukui function-provided that one is willing to allow for the Fukui function to be negative. Negative Fukui functions emerge as key indicators of redox-induced electron rearrangements, where oxidation of an entire molecule (acetylene) leads to reduction of a specific region of the molecule (along the bond axis, between the carbon atoms). Remarkably, further oxidization of these substituted acetylenes (one can remove as many as four electrons!) causes the electron density along the C-C bond to increase even more. This work provides substantial evidence that the molecular Fukui function is sometimes negative and reveals that this is due to orbital relaxation.

Critical thoughts on computing atom condensed Fukui functions

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory.

Computing Fukui functions without differentiating with respect to electron number. I. Fundamentals

By using perturbations in the molecular external potential, the authors deduce the Fukui function from the change in Kohn-Sham orbital energies, avoiding the troublesome differentiation of the density with respect to electron number. Though this paper focuses on the Fukui function, the same general technique can be used to compute the functional derivative of any observable with respect to the external potential. In this paper, the method is used to compute the Fukui function for the beryllium atom and the formaldehyde molecule. The follow-up paper (part II) addresses the problem of computing condensed reactivity indicators.

Computing Fukui functions without differentiating with respect to electron number. II. Calculation of condensed molecular Fukui functions

The Fukui function is a frequently used DFT concept in the description of a system's regioselective preferences to undergo electrophilic, nucleophilic, or radical attacks. Until now, this function has usually been evaluated using finite difference approximations. The first paper in this series proposed a method for obtaining the Fukui function by a direct calculation of the functional derivative of the chemical potential with respect to the external potential. This paper extends the method to condensed Fukui functions and applies it to an extensive testing set of molecules. Results are promising, which demonstrates the usefulness of the new formalism.

Chemical hardness and the discontinuity of the Kohn-Sham exchange-correlation potential

Chemical hardness, identified as the difference between the vertical first ionization potential I and the vertical electron affinity A, is analyzed in the context of the ionization theorems to derive expressions for its evaluation at different levels of approximation that arise as a direct consequence of the derivative discontinuity of the exchange-correlation potential. The quantities involved in these expressions incorporate indirectly the effects of the discontinuity, but their values may be calculated with any functional of the local density approximation, generalized gradient approximation, or optimized effective potential type, with or without derivative discontinuity, and with or without the correct asymptotic behavior. By comparison with the vertical energy difference values of I and A, which requires the calculation of the N-, (N-1)-, and (N+1)-electron systems, it is found, for a set of 14 closed shell molecules, that the difference between the eigenvalues of the highest occupied molecular orbitals of the N- and (N+1)-electron systems leads to rather accurate values, when the correct asymptotic behavior is incorporated, and that a second-order one-body perturbation approach that only requires information from the N-electron system leads to reasonable values.

Predicting the reactivity of ambidentate nucleophiles and electrophiles using a single, general-purpose, reactivity indicator

We recently proposed a new reactivity indicator, termed the "general-purpose reactivity indicator", Xi, which describes not only the classical reactivity paradigms, but also describes reactions that are neither frontier-orbital nor electrostatically controlled. This indicator was proposed to be especially useful for reactants with multiple reactive sites, especially if the nature of the reactivity at those sites was different. This suggests that this reactivity indicator is especially appropriate for ambidentate molecules; this paper confirms this hypothesis. The general-purpose reactivity indicator not only identifies the most reactive sites, it also identifies which substrates prefer which reactive sites. In particular, the reactivity indicator allows one to clearly distinguish which sites of an ambidentate molecule are most reactive when electron transfer from the attacking reagent is large (a soft reagent) and which sites are most reactive when the attacking reagent is hard and highly charged (so that electron transfer is relatively insignificant). To illustrate the efficacy of the indicator for nucleophiles we consider SCN(-), SeCN(-), NO(2)(-), SO(3)(2-). For electrophiles we consider dimethyl carbonate, N-methyl-N-nitrosotoluene-p-sulfonamide (MNTS), and 1-chloro-2,4,6-trinitrobenzene (CNB).