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While high-pressure chemistry has a well-established history, methods to simulate pressure at the single-molecule level have been somewhat lacking. The current work aims at comparing two static models (XP-PCM and GOSTSHYP) to apply isotropic pressure to single molecules, focusing on the equilibrium bond length and electric dipole moment of diatomic molecules. Numerical challenges arising in the potential energy surface using the XP-PCM method were examined, and a pragmatic approach was followed to mitigate these. The definition of the cavity was scrutinized, and two approaches to retrieve the isotropic character that could potentially be lost when using the standard methodology were suggested. Subsequently, equilibrium bond lengths under pressure were evaluated, showing reasonable agreement between GOSTSHYP and XP-PCM, but some discrepancies persist. A Taylor series analysis introduced elsewhere was then applied to rationalize the observed trends in terms of the bond surface. Finally, the dipole moment was shown to be highly sensitive to the cavity definition, and qualitative agreement necessitates the use of our adapted procedure.

In the context of the growing impact of conceptual density functional theory (DFT) as one of the most successful chemical reactivity theories, response functions up to second order have now been widely applied; in recent years, among others, particular attention has been focused on the linear response function and also extensions to higher order have been put forward. As the larger part of these studies have been carried using a finite difference approach to compute these concepts, we now embarked on (an extension of) an analytical approach to conceptual DFT. With the ultimate aim of providing a complete set of analytically computable second order properties, including the softness and hardness kernels, the hardness as the simplest second order response function is scrutinized again with numerical results highlighting the difference in nature between the analytical hardness (referred to as hardness condition) and the Parr-Pearson absolute chemical hardness. The hardness condition is investigated for its capability to gauge the (de)localization error of density functional approximations (DFAs). The analytical Fukui function, besides overcoming the difficulties in the finite difference approach in treating negatively charged systems, also showcases the errors of deviating from the straight-line behavior using fractional occupation number calculations. Subsequently, the softness kernel and its atom-condensed inverse, the hardness matrix, are accessed through the Berkowitz-Parr relation. Revisiting the softness kernel confirms and extends previous discussions on how Kohn’s Nearsightedness of Electronic Matter principle can be retrieved and identified as the physicist’s version of the chemist’s “transferability of functional groups” concept. The accurate, analytical hardness matrix evaluation on the other hand provides further support for the basics of Nalewajski’s charge sensitivity analysis. Based on Parr and Liu’s functional expansion of the energy functional, a new energy decomposition is introduced with an order of magnitude analysis of the different terms for a series of simple molecules both at their equilibrium geometry and upon variation in bond length and dihedral angle. Finally, for the first time, the perturbation expansion of the energy functional is studied numerically up to second order now that all response functions and integration techniques are at hand. The perturbation expansion energies are in excellent agreement with those obtained directly from DFA calculations giving confidence in the convergence of the perturbation series and its use in judging the importance of the different terms in reactivity investigations.

The linear response kernel also referred to as linear response function (LRF) in the framework of conceptual density functional theory has gained tremendous success in time-dependent density functional theory. Comparatively less attention has been devoted to the LRF from a chemical reactivity perspective in its time- or frequency-independent context, although it has recently been used to qualitatively describe electron delocalization, (anti-)aromaticity, inductive and mesomeric effects, etc. Despite these successes, which were obtained by approximating the LRF using the independent particle approximation deriving from a coupled-perturbed Kohn–Sham computation, the robustness of this LRF approach needs to be assessed. In this work, we compute the LRF at four levels of approximation (independent particle approximation, random phase approximation, Hartree–Fock approximation, and the (exact) DFT (density functional theory) expression) using functionals from the first four rungs of Jacob’s ladder of exchange-correlation energy functionals. To scrutinize the impact of these approximations, new visualization strategies are discussed and systematized. The overall conclusion is that the independent particle approximation yields qualitatively correct results (ergo previous conceptual applications of the LRF are trustworthy), but for quantitative results, LRF expressions including coulomb and exchange(-correlation) terms should be included. With respect to functionals, density-gradient contributions to the exchange-correlation kernel are less than 10% and may be omitted safely where that is preferable computationally.

With the idea of using alchemical derivatives to explore in an efficient, computer- and cost-effective way Chemical Space was launched several years ago. In the context of Conceptual DFT response functions, these energies vs nuclear charge derivatives permit the estimatation of the energy of transmutants of a given starting or reference molecule showing different nuclear compositions. After an explorative study on small and planar molecules (Balawender et al. J. Chem. Theory Comput.2013, 9, 5327) by the present authors of this paper, the present study fully exploits the computational advantages of the alchemical derivatives in larger three-dimensional systems. Starting from a single reference calculation on C60, the complete BNsubstitution pattern, from single substituted C58BNvia the belt (C20(BN)20and the ball C12(BN)24structures to the fully substituted (BN)30, is explored. Successive and simultaneous substitution strategies are followed and compared, indicating that both techniques yield identical results up to 13 substitutions but that for higher substitutions the simultaneous approach needs to be taken. Due to the cost-efficiency of the algorithm this path can indeed be followed as opposed to earlier work in the literature where for each step a full SCF calculation was at stake leading to prohibitively large computational demands for adopting the simultaneous approach. Previously formulated rules governing the substitution pattern by Kar and co-workers are scrutinized in this context and reformulated giving chemical insight in the gradual substitution process and the relative energies of the isomers. In its present form the method offers an interesting venue to study BN substitution patterns in higher fullerenes and graphene and in general paves the way for more efficient exploration of the Chemical Space.

In this paper, we verify the usefulness of the alchemical derivatives in the prediction of chemical properties. We concentrate on the stability of the transmutation products, where the term “transmutation” means the change of the nuclear charge at an atomic site at constant number of electrons. As illustrative transmutations showing the potential of the method in exploring chemical space, we present some examples of increasing complexity starting with the deprotonation, continuing with the transmutation of the nitrogen molecule, and ending with the substitution of isoelectronic B–N units for C–C units and N units for C–H units in carbocyclic systems. The basis set influence on the qualitative and quantitative accuracies of the alchemical predictions was investigated. The alchemical deprotonation energy (from the second order Taylor expansion) correlates well with the vertical deprotonation energy and can be used as a preliminary indicator for the experimental deprotonation energy. The results of calculations for the BN derivatives of benzene and pyrene show that this method has great potential for efficient and accurate scanning of chemical space.

Although a lot of work has been done on the chemical relevance of the atom-condensed linear response kernel χABregarding inductive, mesomeric, and hyperconjugative effects as well as (anti)aromaticity of molecules, the same cannot be said about its not condensed form χ(r,r′). Using a single Slater determinant KS type ansatz involving second order perturbation theory, we set out to investigate the linear response kernel for a number of judiciously chosen closed (sub)shell atoms throughout the periodic table and its relevance, e.g., in relation to the shell structure and polarizability. The numerical results are to the best of our knowledge the first systematic study on this noncondensed linear response function, the results for He and Be being in line with earlier work by Savin. Different graphical representations of the kernel are presented and discussed. Moreover, a frontier orbital approach has been tested illustrating the sensitivity of the nonintegrated kernel to the nodal structure of the orbitals. As a test of our method, a numerical integration of the linear response kernel was performed, yielding an accuracy of 10–4. We also compare calculated values of the polarizability tensor and their evolution throughout the periodic table to high-level values found in the literature.

The concept of the atomic charge is extensively used to model the electrostatic properties of proteins. Atomic charges are not only the basis for the electrostatic energy term in biomolecular force fields but are also derived from quantum mechanical computations on protein fragments to get more insight into their electronic structure. Unfortunately there are many atomic charge schemes which lead to significantly different results, and it is not trivial to determine which scheme is most suitable for biomolecular studies. Therefore, we present an extensive methodological benchmark using a selection of atomic charge schemes [Mulliken, natural, restrained electrostatic potential, Hirshfeld-I, electronegativity equalization method (EEM), and split-charge equilibration (SQE)] applied to two sets of penta-alanine conformers. Our analysis clearly shows that Hirshfeld-I charges offer the best compromise between transferability (robustness with respect to conformational changes) and the ability to reproduce electrostatic properties of the penta-alanine. The benchmark also considers two charge equilibration models (EEM and SQE), which both clearly fail to describe the locally charged moieties in the zwitterionic form of penta-alanine. This issue is analyzed in detail because charge equilibration models are computationally much more attractive than the Hirshfeld-I scheme. Based on the latter analysis, a straightforward extension of the SQE model is proposed, SQE+Q0, that is suitable to describe biological systems bearing many locally charged functional groups.

In this work, we present a novel model, referred to as BH-DFT-D, for the evaluation of London dispersion, with the purpose to correct the performance of local DFT exchange-correlation functionals for the description of van der Waals interactions. The new BH-DFT-D model combines the equations originally derived by Buckingham [Buckingham, A. D. Adv. Chem. Phys1967, 12, 107] with the definition of distributed multipole polarizability tensors within the Hirshfeld method [Hirshfeld, F.L. Theor. Chim. Acta1977, 44, 129], resulting in nonlocal, fully anisotropic expressions. Since no damping function has been introduced yet into the model, it is suitable in its present form for the evaluation of dispersion interactions in van der Waals dimers with no or negligible overlap. The new method is tested for an extended collection of van der Waals dimers against high-level data, where it is found to reproduce interaction energies at the BH-B3LYP-D/aug-cc-pVTZ level with a mean average error (MAE) of 0.20 kcal/mol. Next, development steps of the model will consist of adding a damping function, analytical gradients, and generalization to a supramolecular system.

Following the increasing interest in the higher-order (functional) derivatives of conceptual density functional theory, we developed and implemented a method for calculating second-order functional derivatives with respect to the external potential. Our method is theoretically exact but involves two numerical approximations: the functional derivatives are expanded in a basis set, and the values of the corresponding expansion coefficients are determined by probing the molecular environment by a finite set of external potential perturbations. Exact solutions are obtained only in the limit of a complete basis set and an infinite number of distinct perturbations. We use this method to compute the atom-condensed linear response kernel for a series of six molecules and show that the results are comparable to the ones obtained by a previously proposed, approximate approach from second-order perturbation theory. The numerical error of the current implementation is about 0.01 au. Because the present method gives exact or quasi-exact solutions, it can be used as a benchmark against which approximate approaches are assessed.

Exploiting the locality of the chemical potential of an excited state when it is evaluated using the ground-state density functional theory (DFT), a new descriptor for excited states has been proposed. This index is based on the assumption that the relaxation of the electronic density drives the chemical reactivity of excited states. The sign of the descriptor characterizes the electrophilic or nucleophilic behavior of the atomic regions. A relation between the new descriptor and the dual descriptor is derived and provides a posteriori justification of its use to rationalize the Woodward−Hoffmann rules for photochemical reactions within the conceptual DFT. Finally, the descriptor is successfully applied to some [2 + 2] photocycloadditions, like Paterno−Büchi reactions.

This paper concerns the accurate description of the surface oxygen reactivity for the alkaline earth metal oxides using local DFT-based reactivity indices. The cumbersome periodic boundary conditions calculations, typically required to probe the reactivity of such systems, are avoided by the construction of a reliable cluster model. The standard Fukui function concept of conceptual DFT is generalized to include the contribution from not only the HOMO and the LUMO but also from other chemically relevant orbitals. Results prove that this approach is a valuable and straightforward alternative to the reactivity calculation of extended systems.

An alternative approach for the calculation of DFT-based reactivity descriptors involving derivatives of the energy with respect to the number of electrons and the external potential is further evaluated. Using functional derivatives with respect to the external potential, the finite difference approximation was avoided for the local calculation of the Fukui functions and the dual descriptor. A relevant set of molecules has been calculated after the optimization of computational parameters. It is shown that the new approach correctly predicts the nucleophilic attack on CH 2O, the formation of CO metal complexes, the regioselectivity of monosubstituted benzenes, and the softest nucleophilic site in some ambident nucleophiles.